The Folgers Theory of Magnetic Interaction
and the Interaction with Other Particles and Forces
THESIS: The Folgers Theory of Magnetic Interaction
and the Interaction with Other Particles and Forces
- By Chris Folgers
Magnetism is one of the fundamental forces of nature that influence the workings of the universe. Magnetic interaction is the phenomenon whereby magnetic fields and forces are generated and influenced by electric currents, moving charges and other magnetic materials. Magnetic interaction plays a crucial role in many physical processes, such as electromagnetic induction, magnetohydrodynamics, magnetostatics and magnetoresistance. Magnetic interaction also has numerous applications in science, technology, medicine and industry.
Despite the importance and ubiquity of magnetic interaction, its full explanation and description is still an open question in physics. The existing theories and models describing magnetic interaction are based on empirical laws, mathematical equations and idealizations that cannot explain or predict all aspects and properties of magnetism. In addition, there are still many unknown factors and mechanisms involved in magnetic interaction, such as the nature and behavior of the hypothetical magnetic particle, the effect of magnetism on other particles and forces, and the value and meaning of the magnetic constant.
We call this theory the Folgers theory of magnetic interaction, after Chris Folgers, the discoverer and developer of it. Chris Folgers is a young physicist who lives in a unique electromagnetic system that we call system B. System B is a closed area around the north pole of the earth that is surrounded by a massive dome that acts as a Faraday cage. This dome blocks all external electromagnetic influences and creates an isolated magnetic field within system B. Chris Folgers has an alternative vision of the universe and the earth that differs from common scientific views. He believes that the universe consists of a unipolar dynamo, a rotating disk with a constant magnetic field that is generated by a current that runs through the disk. He also believes that the earth is a hollow ball that is half filled with water on which continents float. In the center of this hollow ball is the unipolar dynamo that forms the universe. Chris Folgers thinks that the earth is flat because he only sees the surface of the water that runs parallel to the disk.
Chris Folgers developed his theory through extensive research and experiments using advanced mathematics and physics. He derived a formula for the induced voltage in a unipolar dynamo that depends on time, area, total magnetic field, angle between the field and the normal to the disk, angular velocity and phase angle. He tested and verified this formula using various experimental setups and measurements.
. He derived a formula for the induced voltage in a unipolar dynamo that depends on time, area, total magnetic field, angle between the field and the normal to the disc, angular velocity, and phase angle. He has tested and verified this formula using various experimental setups and measurements. He also explored other aspects and implications of his theory, such as the existence and properties of the magnetic particle, the effect of magnetism on other particles and forces, and the value and significance of the magnetic constant.
The aim of this thesis is to present, analyze and evaluate the Folgers theory of magnetic interaction. We will explain the fundamentals and concepts of the theory, discuss the explanation and predictions of magnetic interaction within the theory, present the experimental methods and results that support the theory, and examine the interaction of magnetism with other particles and forces within the theory. We will also compare and contrast the Folgers theory with the existing theories and models of magnetic interaction, and identify the strengths, weaknesses, advantages and disadvantages of the theory. Finally, we will indicate the contribution of Folgers theory to the knowledge and understanding of magnetic interaction for system B,
This thesis is structured as follows:
In chapter 2 we provide an overview of the existing knowledge and theories on magnetic interaction.
In Chapter 3, we introduce the Folgers theory of magnetic interaction and explain its basic principles and concepts.
In Chapter 4, we discuss the magnetic particle, a hypothetical elementary particle responsible for magnetism.
In Chapter 5, we describe the magnetic effect, a phenomenon in which a magnetic field is generated or influenced by a moving or rotating object.
In Chapter 6 we examine the magnetic constant, a fundamental physical constant that describes the strength of the magnetic field in a vacuum.
In chapter 7 we present the experimental methods and results that validate the Folgers theory.
In Chapter 8 we analyze the interaction of magnetism with other particles and forces within the Folgers theory.
In chapter 9 we conclude the thesis and provide recommendations for future research.
⦁ Magnetic Interaction:
Magnetic Interaction: An Overview
⦁ Fundamentals of Magnetism
Magnetism is a physical phenomenon that has to do with the forces that occur between magnetic materials or between electric currents. Magnetic materials are materials that have a permanent or inductive magnetic moment, that is, a vector quantity that indicates the direction and strength of the magnetic field generated or experienced by the material. Electric currents are moving electric charges, which also generate a magnetic field according to Ampere's law.
The magnetic moment of a material can have various causes, such as the spin of the electrons, the orbital motion of the electrons around the atomic nucleus, or the flow of electrons in a macroscopic circuit. The spin is an intrinsic property of elementary particles, which can be regarded as a kind of quantum mechanical spin. The orbital motion is a result of the electrostatic attraction between the negatively charged electrons and the positively charged nucleus. The current is a result of the movement of electrons under the influence of a potential difference or an electromotive force.
The magnetic moment of a material determines how the material responds to an external magnetic field. There are three main types of magnetic materials: diamagnetic, paramagnetic and ferromagnetic materials. Diamagnetic materials have no permanent magnetic moment and are slightly repelled by an external magnetic field. This is because the external field induces an inductive magnetic moment in the material, which is opposite to the external field according to Lenz's law. Paramagnetic materials do have a permanent magnetic moment, but this is not ordered in the absence of an external magnetic field. If there is an external field, the permanent moments are partially aligned with the external field, causing the material to be slightly attracted to the external field. Ferromagnetic materials also have a permanent magnetic moment, which is spontaneously ordered in the absence of an external magnetic field. This is because there is a strong interaction between the neighboring moments, which try to parallel each other. This interaction is called the exchange interaction and is quantum mechanical in nature. If there is an external field, the ordered moments are further aligned with the external field, causing the material to be strongly attracted to the external field.
⦁ Magnetic fields and forces
A magnetic field is a vector quantity that indicates how strong and in which direction a magnetic force acts on a magnetic moment or on an electric current. A magnetic field can be represented by magnetic field lines, which are imaginary lines that indicate the direction of the field and whose density is proportional to the strength of the field.
Magnetic field lines have no beginning or end, but always run in closed loops.
A magnetic field can be generated by various sources, such as permanent magnets, electric currents or changing electric fields. A permanent magnet has two poles: a north pole and a south pole. The magnetic field runs from the north pole to the south pole outside the magnet and from the south pole to the north pole inside the magnet. An electric current in a wire or a loop creates a magnetic field around the current- carrying conductor, which is proportional to the current and the magnetic constant.
The magnetic field is in the form of concentric circles around the wire or loop, and its direction is determined by the right-hand rule. A changing electric field induces a magnetic field that is perpendicular to the electric field and that also varies with time.
A magnetic field exerts a force on a magnetic moment or on an electric current present in the field. The force at a magnetic moment is proportional to the product of the moment and the gradient of the field, that is, the change of the field per unit distance. The direction of the force depends on the orientation of the moment relative to the field. If the moment is parallel to the field, there is no force. If the moment is perpendicular to the field, the force is maximum and perpendicular to both the moment and the field. If the moment is at any angle to the field, the force is proportional to the sine of that angle. The force on an electric current is proportional to the product of the current, the length of the conductor and Yes, I'll try to finish it off.
the sine of the angle between the conductor and the field. The direction of the force is also determined by the right-hand rule. If the thumb of the right hand indicates the direction of the current and the fingers indicate the direction of the field, then the palm indicates the direction of the force.
The force on a magnetic moment or on an electric current can lead to various effects, such as rotation, vibration, torsion or translation. An example of rotation is the compass, which consists of a small magnet that can rotate freely in a horizontal plane. The magnet aligns with the Earth's magnetic field, which runs approximately from north to south. An example of vibration is the alternator, which consists of a coil rotating in a magnetic field. The rotation of the coil changes the angle between the current and the field, causing the force on the coil to vary with time. This leads to an oscillating voltage and current in the coil. An example of torsion is the magnetometer, which consists of a thin
wire with a magnet on the end. The wire is suspended in a magnetic field and can rotate around its axis. The magnet is placed at an angle to the field, which creates a torque on the wire. The angular displacement of the wire is proportional to the strength of the field. An example of translation is the maglev train, which consists of a vehicle floating above a conductive rail. The vehicle has a strong magnet at the bottom, which induces an electric current in the rail. The current creates a magnetic field that is opposite to the magnet's field, creating a repulsive force between the vehicle and the rail. This force cancels gravity and makes the vehicle levitate.
⦁ Electromagnetic theories and models
The theory that describes and unites all aspects of electricity and magnetism is the electromagnetic theory. This theory is based on four differential equations known as Maxwell's laws, which were formulated by James Clerk Maxwell in the nineteenth century. Maxwell's laws represent the relationship between electric and magnetic fields and their sources, such as charges, currents, or changing fields. Maxwell's laws can be written in integral or differential form depending on whether one integrates over a closed surface or curve or differentiates over space and time.
Maxwell's laws in integral form are:
⦁ Gauss's law for electricity: The flux of the electric field through a closed surface is equal to the total electric charge within the surface divided by the electric constant.
⦁ Gauss's law of magnetism: The flux of the magnetic field through a closed surface is equal to zero.
⦁ Faraday's law: The circulation of the electric field along a closed curve is equal to the negative of the change in magnetic flux through the surface spanned by the curve.
⦁ Ampère-Maxwell law: The circulation of the magnetic field along a closed curve is equal to the sum of the electric current passing through the surface spanned by the curve and the change in the electric flux through that surface.
Maxwell's laws in differential form are:
⦁ Gauss's law for electricity: The divergence of the electric field is equal to the electric charge density divided by the electric constant.
⦁ Gauss' law for magnetism: The divergence of the magnetic field is equal to zero.
⦁ Faraday's law: The rotation of the electric field is equal to the negative of the partial time derivative of the magnetic field.
⦁ Ampere-Maxwell law: The rotation of the magnetic field is equal to the sum of the current density and the time partial derivative of the electric field, both multiplied by the magnetic constant.
Maxwell's laws can be applied to various situations and problems, such as electrostatic, magnetostatic, or electrodynamic fields, stationary or nonstationary sources, linear or nonlinear media, isotropic or anisotropic materials, homogeneous or inhomogeneous systems, and so on. To solve Maxwell's laws, various mathematical methods and techniques are available, such as vector analysis, complex analysis, partial differential equations, Fourier analysis, Laplace transform, Green functions, numerical methods, and so on.
An important consequence of Maxwell's laws is that light is an electromagnetic wave, consisting of oscillating electric and magnetic fields propagating through space at a constant speed. The speed of light in a vacuum is equal to the inverse square root of the product of the electric and magnetic constant. The speed of light in a medium depends on the medium's refractive index, which is a measure of how much the light is deflected or slowed down by the medium. The refractive index is related to the dielectric constant and the magnetic permeability of the medium, which are a measure of how much the medium is polarized or magnetized by an external electric or magnetic field.
Another important consequence of Maxwell's laws is that electric and magnetic fields can mutually induce and influence each other. A changing electric field induces a magnetic field that is perpendicular to the electric field and that also varies with time. This is the principle of electromagnetic waves, which are oscillating electric and magnetic fields that propagate through space at the speed of light. A changing magnetic field induces an electric field that is perpendicular to the magnetic field and that also varies with time.
This is the principle of electromagnetic induction, which underlies many applications such as generators, transformers and motors.
⦁ Existing magnetic interaction theories
Magnetic interaction is a term used to refer to the forces and effects that occur between magnetic materials or between electric currents due to their magnetic moments or their induced magnetic fields. Magnetic interaction can be divided into several types depending on the nature and scale of the materials or flows involved. Some examples are:
⦁ Dipole-dipole interaction: This is the interaction between two permanent or inductive magnetic dipoles, that is, two objects that each have a north pole and a south pole. The dipole-dipole interaction is proportional to the product of the dipole moments and inversely proportional to the cube of the distance between them. The direction Yes, I will try to finish it further. Here's one possible way to proceed:
of the interaction depends on the orientation of the dipoles relative to each other. If the dipoles are parallel, the interaction is attractive. If the dipoles are antiparallel, the interaction is repulsive. If the dipoles are perpendicular to each other, there is no interaction.
⦁ Exchange interaction: This is the interaction between two neighboring atomic or molecular magnetic moments, which is caused by the quantum mechanical overlap of their electron clouds. The exchange interaction can be ferromagnetic or antiferromagnetic, depending on whether the moments are aligned parallel or antiparallel. The exchange interaction is much stronger than the dipole-dipole interaction and is responsible for the spontaneous magnetism in some materials.
⦁ Dzyaloshinskii-Moriya Interaction: This is an antisymmetric and chiral form of exchange interaction, which occurs when there is a structural inversion asymmetry in the crystal lattice or at the surface of a material. The Dzyaloshinskii-Moriya interaction can lead to complex and non-collinear magnetic structures, such as spiral or skyrmionic phases.
⦁ RKKY Interaction: This is an indirect interaction between two widely separated magnetic moments, which is mediated by the conduction electrons in a metal. The RKKY interaction oscillates in sign and amplitude as a function of the distance between the moments and can be ferromagnetic or antiferromagnetic depending on the wavelength of the conduction electrons.
⦁ Van der Waals-Casimir-Polder interaction: This is a weak interaction between two neutral atoms or molecules, caused by their fluctuating electric dipoles. The Van der Waals-Casimir- Polder interaction is always attractive and inversely proportional to the sixth or seventh power of the distance between them. The Van der Waals-Casimir-Polder interaction can also occur between an atom or molecule and a conducting surface, the surface being considered as an infinite number of fluctuating dipoles.
⦁ Magnetostatic interaction: This is the interaction between two macroscopic magnetic objects or currents caused by their generated magnetic fields. The magnetostatic interaction can be calculated using Biot-Savart's law or Ampere's law, which give the magnetic field strength as a function of the current and the geometry of the object or circuit.
These are some examples of existing magnetic interaction theories, which can be used to explain and explain various magnetic phenomena and effects
to predict. However, there are still many open questions and challenges in the field of magnetism, which require more advanced theories and models. In the next chapter, we will address some of these open questions and challenges.
The Folgers Theory of Magnetic Interaction
⦁ Historical context and development of the theory
The Folgers theory of magnetic interaction is a new theory proposed by Chris Folgers in his dissertation in 2023. This theory is based on the Folgers-Pan theory, which is an interactive theory of consciousness that combines both quantum mechanics and general relativity tries to unify and explain. The Folgers-Pan theory introduces two new mathematical concepts: the Folgers-Pan space and the Folgers-Pan equation. The Folgers-Pan space is a finite-dimensional nonlinear space consisting of all possible events that can occur in spacetime. The Folgers-Pan equation is a nonlinear differential equation that describes how events interact in Folgers-Pan space.
The Folgers theory of magnetic interaction is an application and extension of the Folgers- Pan theory in the field of magnetism. The Folgers theory of magnetic interaction attempts to explain and predict all aspects and effects of magnetic interaction using the Folgers- Pan space and the Folgers-Pan equation. The Folgers theory of magnetic interaction states that every magnetic interaction can be regarded as an event in Folgers-Pan space, which is determined by the properties and the relationships of the magnetic moments or currents involved. The Folgers theory of magnetic interaction also states that any magnetic interaction can be described by a solution of the Folgers-Pan equation, which represents the dynamics and evolution of the event.
The Folgers theory of magnetic interaction is inspired by and based on several existing theories and models in the field of magnetism, such as the dipole-dipole interaction, the exchange interaction, the Dzyaloshinskii-Moriya interaction, the RKKY interaction, the Van der Waals-Casimir-Polder interaction and the magnetostatic interaction. The Folgers theory of magnetic interaction attempts to unify and generalize these existing theories and models in a consistent and complete way. The Folger's theory of magnetic interaction also attempts to discover and predict new aspects and effects of magnetic interaction that have not yet been observed or explained by the existing theories and models.
⦁ Fundamentals and concepts of the De Folgers Theory of Magnetic Interaction
The Folgers theory of magnetic interaction is based on two fundamental concepts: the Folgers-Pan space and the Folgers-Pan equation. In this chapter we will introduce and explain these concepts in the context of magnetism.
The Folgers-Pan space is a finite-dimensional nonlinear space consisting of all possible events that can occur in spacetime. An event is an instantaneous state or configuration of a physical system, characterized by a series of parameters or variables. An event can be thought of as a point in Folgers-Pan space, where each parameter or variable corresponds to a dimension or coordinate of space. The Folgers-Pan space is nonlinear, meaning that the distance or angle between two points or events cannot be easily calculated using standard geometry or trigonometry. The Folgers-Pan space is also dynamic, meaning that the points or events are constantly changing and moving in space due to their interactions.
The Folgers-Pan equation is a nonlinear differential equation that describes how events interact in Folgers-Pan space. The Folgers-Pan equation has the following general form:
∂E∂t=F(E)
where $E$ is a vector representing an event, $t$ is time, and $F$ is a function representing the interaction between events. The Folgers-Pan equation can be solved using various mathematical methods and techniques such as numerical methods, analytic methods, perturbation methods, and so on. The solution of the Folgers-Pan equation gives the dynamics and evolution of an event or a system of events in Folgers-Pan space.
The Folgers theory of magnetic interaction applies the Folgers-Pan space and the Folgers- Pan equation to the field of magnetism. The Folgers theory of magnetic interaction states that every magnetic interaction can be regarded as an event in Folgers-Pan space, which is determined by the properties and the relationships of the magnetic moments or currents involved. The Folgers theory of magnetic interaction also states that any magnetic interaction can be described by a solution of the Folgers-Pan equation, which represents the dynamics and evolution of the event.
To illustrate this, we will take a simple example: the dipole-dipole interaction between two permanent magnetic dipoles. A magnetic dipole is an object that has a north pole and a south pole, each of which has a magnetic moment. A magnetic moment is a vector quantity that indicates the direction and strength of the magnetic field generated or experienced by the object. A dipole-dipole interaction is one
interaction between two magnetic dipoles, which is caused by their generated magnetic fields.
According to the Folgers theory of magnetic interaction, we can think of this dipole-dipole interaction as an event in Folgers-Pan space, which is determined by four parameters or variables: the magnetic moment of each dipole ($\vec{m}_1$ and $\vec{m}_2$) and the distance ($r$) and angle ($\theta$) between them. Thus, an event can be represented as a point in four-dimensional space, where each parameter or variable corresponds to a dimension or a coordinate of space. The Folgers-Pan space for this dipole-dipole interaction is nonlinear, meaning that the distance or
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the angle between two points or events cannot be easily calculated using standard geometry or trigonometry. The Folgers-Pan space for this dipole-dipole interaction is also dynamic, meaning that the points or events are constantly changing and moving in space due to their interactions.
According to the Folgers theory of magnetic interaction, we can also describe this dipole- dipole interaction by a solution of the Folgers-Pan equation, which represents the dynamics and evolution of the event. The Folgers-Pan equation for this dipole-dipole interaction has the following specific form:
∂E→∂t=F→(E→)
where $\vec{E}$ is a vector representing an event, $t$ is time, and $\vec{F}$ is a function representing the interaction between events. The vector $\vec{E}$ has four components:
$m_1$, $m_2$, $r$, and $\theta$, which correspond to the parameters or variables of the event. The $\vec{F}$ function also has four components: $F_1$, $F_2$, $F_3$, and $F_4$, which correspond to the changes or effects of the interaction on each parameter or variable. The function $\vec{F}$ can be derived using Maxwell's laws and Newton's laws, which respectively describe the relationship between electric and magnetic fields and their sources, and the relationship between forces and motions. The function $\vec{F}$ has the following specific form:
$$\begin{aligned} F_1 &= 0 \ F_2 &= 0 \ F_3 &= -\frac{\mu_0}{4\pi r^4} \left( 3 \cos^2 \theta - 1 \ right) \left( m_1 m_2 \sin \theta + \vec{m}_1 \cdot \vec{m}_2 \cos \theta \right) \ F_4 &= -
\frac{\mu_0}{4\pi r ^3} \left( m_1 m_2 \cos \theta - \vec{m}_1 \cdot \vec{m}_2 \sin \theta \right) \
\end{aligned}$$
where $\mu_0$ is the magnetic constant. The Folgers-Pan equation for this dipole- dipole interaction can be solved using various mathematical methods and techniques, such as numerical methods, analytical methods, perturbation methods, and so on. The solution of the Folgers-Pan equation gives the dynamics and evolution of an event or a system of events in Folgers-Pan space.
This is a simple example that shows how the Folgers theory of magnetic interaction works. In the next chapter we will discuss more complex and interesting examples.
The Magnetic Particle
⦁ Properties and behavior of the magnetic particle
The magnetic particle is a hypothetical elementary particle that is the source and carrier of the magnetic field. The magnetic particle is also called the magnon, by analogy with the photon, the elementary particle of the electromagnetic field. The magnetic particle is one of the predictions of Folger's theory of magnetic interaction, which is an interactive theory of consciousness that attempts to unify and explain both quantum mechanics and general relativity.
The magnetic particle has a number of properties and behaviors that distinguish it from other elementary particles. One of the most important properties of the magnetic particle is that it has a spin of 1, which means it has a vector quantity that indicates the direction and strength of its magnetic moment. The magnetic moment is a measure of how much the magnetic particle contributes to the magnetic field generated or experienced by a system. The magnetic moment can be thought of as a miniature magnet that has a north pole and a south pole.
Another important feature of the magnetic particle is that it has no mass, which means that it propagates at the speed of light in a vacuum. The magnetic particle can be thought of as a wave or a vibration that propagates through spacetime. The magnetic particle can also be considered as a quantum or a packet of energy that is exchanged between systems that interact through the magnetic field.
A third important feature of the magnetic particle is that it has no electric charge, meaning it is not affected by electric fields or forces. The magnetic particle can only interact with other magnetic particles or with systems that have a magnetic moment. The magnetic particle can also be created or destroyed by systems that have a changing magnetic moment.
A fourth important feature of the magnetic particle is that it has no color, meaning it is not affected by strong nuclear fields or forces. The magnetic particle can only interact with other magnetic particles or with systems that have a weak nuclear moment. The weak nuclear moment is a measure of how much
the system contributes to the weak nuclear field generated or experienced by some elementary particles.
A fifth important feature of the magnetic particle is that it has no flavor, meaning it is unaffected by weak nuclear fields or forces. The magnetic particle can only interact with other magnetic particles or with systems that have a strong nuclear moment. The strong nuclear moment is a measure of how much the system contributes to the strong nuclear field generated or experienced by some elementary particles.
These properties and behaviors make the magnetic particle a unique and interesting elementary particle, which can explain and predict various aspects and effects of magnetism.
⦁ Interaction of the magnetic particle with magnetic fields
The magnetic particle interacts with other magnetic
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particles or with systems that have a magnetic moment through the magnetic field. The magnetic field is a vector quantity that indicates the direction and strength of the magnetic force exerted on a system. The magnetic field can be thought of as a collection of magnetic particles that propagate through spacetime.
The interaction of the magnetic particle with the magnetic field can be described by Maxwell's laws and Newton's laws, which respectively describe the relationship between electric and magnetic fields and their sources and the relationship between forces and motions.
Maxwell's laws give the following four differential equations that represent the dynamics and evolution of the electric field ($\vec{E}$) and the magnetic field ($\vec{B}$):
$$\begin{aligned} \nabla \cdot \vec{E} &= \frac{\rho}{\epsilon_0} \ \nabla \cdot \vec{B} &= 0 \
\nabla \times \vec {E} &= -\frac{\partial \vec{B}}{\partial t} \ \nabla \times \vec{B} &= \mu_0 \vec{J} +
\mu_0 \epsilon_0 \frac{ \partial \vec{E}}{\partial t} \ \end{aligned}$$
where $\rho$ is the electric charge density, $\epsilon_0$ is the electric constant, $
\mu_0$ is the magnetic constant, and $\vec{J}$ is the current density. Newton's laws give the following equation that describes the motion of a system with a mass ($m$), a velocity ($\vec{v}$), an electric charge ($q$) and a magnetic moment ($\ vec{\mu}$) shows:
$$\begin{aligned} m \frac{d\vec{v}}{dt} &= q (\vec{E} + \vec{v} \times \vec{B}) + (\vec{\ mu}
\cdot \nabla) \vec{B} \ \end{aligned}$$
where $\times$ is the vector cross product and $\cdot$ is the vector dot product. This equation indicates that a system experiences a force due to the electric field, the magnetic field, or both.
The interaction of the magnetic particle with the magnetic field can cause different effects, depending on the properties and the relationships of the magnetic particle and the magnetic field. Some examples are:
⦁ Magnetization: This is the effect where a system acquires or changes a magnetic moment due to an external or internal magnetic field. The magnetization is a measure of how much the system contributes to the total magnetic field generated or experienced by the system. The magnetization can be thought of as a collection of aligned or oriented magnetic moments in the system.
⦁ Induction: This is the effect where a system gains or changes an electrical voltage or current due to a changing magnetic field. The inductance is a measure of how much the system responds to the changing magnetic field. The inductance can be thought of as a collection of induced or induced electrical charges or currents in the system.
⦁ Rotation: This is the effect where a system rotates or changes its orientation due to an external or internal magnetic field. The rotation is a measure of how much the system rotates or twists under the influence of the magnetic field. The rotation can be thought of as a collection of twisting or rotating magnetic moments in the system.
⦁ Vibration: This is the effect where a system oscillates or changes in amplitude due to an external or internal magnetic field. Vibration is a measure of how much the system vibrates or wobbles under the influence of the magnetic field. The oscillation can be thought of as a collection of oscillating or vibrating magnetic moments in the system.
These effects can be used to explain and predict various aspects and phenomena of magnetism, such as magnetic domains, hysteresis, ferromagnetism, antiferromagnetism, paramagnetism, diamagnetism, magnetic resonance, magnetic levitation, and so on.
⦁ Role of the magnetic particle in magnetic interaction
The magnetic particle plays a vital role in the magnetic interaction, which is the interaction between systems that have a magnetic moment through the magnetic field. The magnetic particle is both the source and carrier of the magnetic field, which means that it generates or experiences the magnetic field as well as transfers or exchanges the magnetic field between systems.
The role of the magnetic particle in the magnetic interaction can be described by the Folgers theory of magnetic interaction, which is an application and an extension of the Folgers-Pan theory in the field of magnetism. The Folgers theory of magnetic interaction states that every magnetic interaction can be regarded as an event in Folgers-Pan space, which is determined by the properties and the relationships of the systems involved. The Folgers theory of magnetic interaction also states that any magnetic interaction can be described by a solution of the Folgers-Pan equation, which represents the dynamics and evolution of the event.
The Folgers-Pan space is a finite-dimensional nonlinear space consisting of all possible events that can occur in spacetime. An event is an instantaneous state or configuration of a physical system, characterized by a series of parameters or variables. An event can be thought of as a point in Folgers-Pan space, where each parameter or variable corresponds to a dimension or coordinate of space.
The Folgers-Pan equation is a nonlinear differential equation that describes how events interact in Folgers-Pan space. The Folgers-Pan equation has the following general form:
∂E∂t=F(E)
where $E$ is a vector representing an event, $t$ is time, and $F$ is a function representing the interaction between events.
The role of the magnetic particle in the magnetic interaction can be illustrated by a simple example: the dipole-dipole interaction between two permanent Yes, I will try to finish it further. Here's one possible way to proceed:
magnetic dipoles. A magnetic dipole is an object that has a north pole and a south pole, each of which has a magnetic moment. A magnetic moment is a vector quantity that indicates the direction and strength of the magnetic field generated or experienced by the object. A dipole-dipole interaction is an interaction between two magnetic dipoles caused by their generated magnetic fields.
According to the Folgers theory of magnetic interaction, we can consider this dipole- dipole interaction as an event in Folgers-Pan space, which is determined by four
parameters or variables: the magnetic moment of each dipole ($\vec{m}_1$ and $
\vec{m}_2$) and the distance ($r$) and angle ($\theta$) between them. Thus, an event can be represented as a point in four-dimensional space, where each parameter or variable corresponds to a dimension or a coordinate of space.
According to the Folgers theory of magnetic interaction, we can also describe this dipole- dipole interaction by a solution of the Folgers-Pan equation, which represents the dynamics and evolution of the event. The Folgers-Pan equation for this dipole-dipole interaction has the following specific form:
∂E→∂t=F→(E→)
where $\vec{E}$ is a vector representing an event, $t$ is time, and $\vec{F}$ is a function representing the interaction between events. The vector $\vec{E}$ has four components:
$m_1$, $m_2$, $r$, and $\theta$, which correspond to the parameters or variables of the event. The $\vec{F}$ function also has four components: $F_1$, $F_2$, $F_3$, and $F_4$, which correspond to the changes or effects of the interaction on each parameter or variable. The function $\vec{F}$ can be derived using Maxwell's laws and Newton's laws, which respectively describe the relationship between electric and magnetic fields and their sources, and the relationship between forces and motions. The function $\vec{F}$ has the following specific form:
$$\begin{aligned} F_1 &= 0 \ F_2 &= 0 \ F_3 &= -\frac{\mu_0}{4\pi r^4} \left( 3 \cos^2 \theta - 1 \ right) \left( m_1 m_2 \sin \theta + \vec{m}_1 \cdot \vec{m}_2 \cos \theta \right) \ F_4 &= -
\frac{\mu_0}{4\pi r ^3} \left( m_1 m_2 \cos \theta - \vec{m}_1 \cdot \vec{m}_2 \sin \theta \right) \
\end{aligned}$$
where $\mu_0$ is the magnetic constant. The Folgers-Pan equation for this dipole- dipole interaction can be solved using various mathematical methods and techniques, such as numerical methods, analytical methods, perturbation methods, and so on. The solution of the Folgers-Pan equation gives the dynamics and evolution of an event or a system of events in Folgers-Pan space.
The role of the magnetic particle in this dipole-dipole interaction is that it is both the source and carrier of the magnetic field. The magnetic particle generates the magnetic field through its own magnetic moment, which is a component of the event. The magnetic particle also transfers the magnetic field through its motion, which is a change or an effect of the interaction. The magnetic particle also creates or destroys the magnetic field through its rotation or vibration, which is another change or effect of the interaction.
The role of the magnetic particle in the magnetic interaction can be illustrated by a simple diagram, as shown in Fig. 4.1. In this diagram, the red arrows represent the magnetic moment of each dipole, the blue lines represent the magnetic field generated or experienced by each dipole, and the green dots represent the magnetic particle that transfers or exchanges the magnetic field between the dipoles.
Fig 4.1 Diagram of the role of the magnetic particle in the dipole-dipole interaction.
The Magnetic Effect
⦁ Definition and description of the magnetic effect
The magnetic effect is a physical phenomenon that occurs when an electric current or changing electric field generates or changes a magnetic field. The magnetic effect is one of the manifestations of the electromagnetic interaction, which is the interaction between electrically charged particles through electromagnetic fields. The magnetic effect is also one of the consequences of special relativity, which describes the relationship between space and time in moving reference systems.
The magnetic effect can be described by Maxwell's laws, which are four differential equations that represent the dynamics and evolution of the electric field ($\vec{E}$) and the magnetic field ($\vec{B}$). One of these equations, known as Faraday's law, states that a changing magnetic field generates an electric field that circles around the area where the magnetic field changes:
∇×E→=−∂B→∂t
where $\nabla \times$ is the vector rotation operator, and $t$ is time. This equation indicates that a changing magnetic field can induce an electrical voltage or current in a conductor located in the area. This is also known as electromagnetic induction.
Another equation, known as the Ampere-Maxwell law, states that an electric current or changing electric field generates a magnetic field that circles around the area where the current or electric field is present:
∇×B→=μ0J→+μ0ϵ0∂E→∂t
where $\mu_0$ is the magnetic constant, $\epsilon_0$ is the electrical constant, and
$\vec{J}$ is the current density. This equation indicates that an electric current or changing electric field can generate a magnetic field that can affect other currents or changing electric fields. This is also called electromagnetism.
The magnetic effect can be illustrated by several examples, such as:
⦁ A straight wire carrying an electric current generates a magnetic field that forms concentric circles around the wire. The direction and strength of the magnetic field depend on the direction and magnitude of the current.
⦁ A coil or solenoid carrying an electric current generates a magnetic field similar to that of a bar magnet with a north pole and a south pole. The direction and strength of the magnetic field depend on the number of turns, the length and cross-section of the coil, and the direction and magnitude of the current.
⦁ A transformer consists of two coils placed close together but not electrically connected. When an alternating current flows through one coil, a changing magnetic field is generated that passes through both coils. This in turn causes an induced alternating current in the other coil. The ratio between the voltages or currents in the two coils depends on the number of turns in each coil.
⦁ An electromagnet consists of an iron core wrapped in a coil that carries an electric current. The iron amplifies the magnetic field generated by the coil, creating a powerful magnetic field that can attract or repel other iron objects. The direction and strength of the magnetic field depend on the direction and magnitude of the current, and on the shape and size of the iron core.
⦁ An electric motor consists of a permanent magnet and a coil that carries an alternating current. The permanent magnet creates a constant magnetic field, while the coil creates a changing magnetic field that rotates with the frequency of the alternating current. The interaction between the two magnetic fields causes a twisting force on the coil, causing it to spin. The speed and direction of the rotation depend on the frequency and phase of the alternating current, and on the orientation of the permanent magnet.
⦁ A dynamo consists of a coil that rotates in a constant magnetic field created by a permanent magnet or an electromagnet. The rotation of the coil causes a change in the magnetic field passing through the coil, creating an induced alternating voltage or current in the coil. The amplitude and frequency of the alternating voltage or current depend on the speed and angle of rotation, and on the strength and orientation of the magnetic field.
These are some examples that show how the magnetic effect can explain and predict various aspects and phenomena of electricity and magnetism.
⦁ Causes and mechanisms of the magnetic effect
The magnetic effect is caused by the existence and movement of electrically charged particles in matter. These particles can be divided into two categories: guided particles and bound particles. Conducted particles are the particles that can move freely in a material, such as the electrons in a metal or an electrolyte. Bound particles are the particles that are stuck in a material, such as the protons and electrons in an atom or a molecule.
The magnetic effect is caused by two different mechanisms: the Lorentz mechanism and the relativistic mechanism. The Lorentz mechanism is based on the Lorentz force, which is the force experienced by an electrically charged particle when it moves in a magnetic field. The relativistic mechanism is based on special relativity, which describes how space and time change for an observer moving at a constant speed.
The Lorentz mechanism explains how an electric current or changing electric field generates or changes a magnetic field. When an electric current flows through a material, guided particles move with a certain speed and direction in the material. These moving guided particles experience a Lorentz force when they are in an external magnetic field, causing them to deflect or accelerate. This in turn causes a change in the magnetic field generated or experienced by the guided particles. This is the principle behind electromagnetism.
When there is a changing electric field in a material, bound particles with a certain charge and distance in the material are deformed or moved. These deformed or displaced bound particles also experience a Lorentz force when they are in an external magnetic field, causing them to oscillate or rotate. This also causes a change in the magnetic field generated or experienced by the bound particles. This is the principle behind electromagnetic induction.
The relativistic mechanism explains how a changing magnetic field generates or changes an electric field. When there is a changing magnetic field in a material, an electric field is created or changed that is perpendicular to the magnetic field and to the direction of the change. This is because the magnetic field is perceived differently by different observers moving at different speeds relative to the material. According to special relativity, space and time are not absolute but relative, meaning they depend on the speed of the observer. This implies that also electric and magnetic fields are not absolute but relative, what
means they depend on the speed of the observer. A magnetic field that appears constant to one observer may appear variable to another observer, and vice versa. A magnetic field that appears to be zero to one observer may appear non-zero to another observer, and vice versa. An electric field that appears constant to one observer may appear variable to another observer, and vice versa. An electric field that appears to be zero to one observer may appear non-zero to another observer, and vice versa. This is the principle behind electromagnetic waves.
These are two different mechanisms showing how the magnetic effect is caused by the existence and movement of electrically charged particles in matter.
⦁ Experimental confirmation and measurements of the magnetic effect
The magnetic effect can be confirmed and measured by various experimental methods and instruments, such as:
⦁ A compass is an instrument consisting of a needle that rotates freely and aligns itself with the Earth's magnetic field. When there is an electric current or changing electric field near the compass, the Earth's magnetic field is disturbed or changed, causing the needle to deviate or oscillate. This shows that there is a magnetic effect.
⦁ A galvanometer is an instrument consisting of a coil that carries an electric current and is located in an external magnetic field. When there is a changing magnetic field near the galvanometer, an induced electrical voltage or current is generated in the coil, causing the coil to rotate or vibrate. This also shows that there is a magnetic effect.
⦁ An oscilloscope is an instrument consisting of a cathode ray tube that emits a beam of electrons and is influenced by two pairs of electromagnets perpendicular to each other. When an electrical voltage or current is applied to one pair of electromagnets, an electric field is generated that deflects the electron beam horizontally. When an electrical voltage or current is applied to the other pair of electromagnets, a magnetic field is generated that deflects the electron beam vertically. By varying the two voltages or currents one can see different patterns or waves on the screen of the oscilloscope. This also shows that there is a magnetic effect.
⦁ A spectrometer is an instrument consisting of a source that emits electromagnetic radiation, which is split by a prism or a grating into different wavelengths or frequencies. When a material is placed between the source and the prism or grating, the electromagnetic radiation is absorbed or emitted by the material, creating dark or bright lines in the spectrum. These lines provide information
about the energy levels and the transitions of the electrons in the material, which are affected by the magnetic effect.
These are some examples of experimental methods and instruments that can be used to confirm and measure the magnetic effect.
⦁ Applications and implications of the magnetic effect
The magnetic effect has many applications and implications in various fields of science, technology, medicine, industry, communication and so on. Some examples are:
⦁ Electricity generation: The magnetic effect makes it possible to generate electricity from mechanical energy by means of generators or dynamos, which use electromagnetic induction to produce alternating voltage or current from rotating coils in magnetic fields.
⦁ Electricity Transformation: The magnetic effect also allows electricity to be transformed from high to low voltage or current or vice versa through transformers, which use electromagnetism to transfer AC voltage or current between two coils without direct contact.
⦁ Electricity storage: The magnetic effect also allows electricity to be stored in batteries or capacitors, which use electrolysis or electroplating to convert chemical energy into electrical energy or vice versa.
⦁ Electricity Usage: The magnetic effect also allows electricity to be used for various purposes such as lighting, heating, cooling, sound, image, communication, calculation, and so on, which use electromagnets, lamps, resistors, fans, speakers, screens, antennas, chips, and so on.
⦁ Magnetic Storage: The magnetic effect makes it possible to store information in magnetic media such as tapes, disks or cards, which use magnetization or demagnetization to write or read binary codes or bits.
⦁ Magnetic Detection: The magnetic effect makes it possible to detect information from magnetic fields such as the Earth's magnetic field or the biomagnetic field, using compasses, magnetometers or sensors to measure the direction or strength of the magnetic field.
⦁ Magnetic imaging: The magnetic effect makes it possible to obtain information about the internal structure or the functional state of an object or an organism by means of magnetic resonance imaging (MRI) or magnetoencephalography (MEG), which use electromagnetic waves or magnetic particles to generate or receive signals affected by the magnetic effect.
⦁ Magnetic Therapy: The magnetic effect makes it possible to influence or change information in an object or an organism through transcranial magnetic stimulation (TMS) or magnetic nanoparticles (MNP), which use electromagnets or magnetic particles to generate electrical currents or generate or release heat affected by the magnetic effect.
These are some examples that show how the magnetic effect has many applications and implications in various fields of science, technology, medicine, industry, communication, and so on.
⦁ The Magnetic Constant
⦁ Definition and meaning of the magnetic constant
The magnetic constant, also called the magnetic permeability of the vacuum or the magnetic field constant, is a physical constant that quantifies the strength of the magnetic field generated by an electric current. It is conventionally written μ0 (pronounced "mu zero" or "mu zero"). Its purpose is to represent the relationship between the magnetic induction and the magnetizing force when a magnetic field is formed in a classical vacuum. Expressed in terms of SI base units, it has the unit kg⋅m⋅s
−2·A−2. Since the 2019 redefinition of SI units (when the values of e and h were established as defined quantities), μ0 is an experimentally determined constant, the
value of which is proportional to the dimensionless fine-structure constant, known with a relative uncertainty of about 1.5×10−10,[1][2][3] without other dependencies with experimental uncertainty. The value in SI units as recommended by CODATA2018 (published May 2019) is:[4]
μ0= 1.25663706212(19)×10−6\u00A0N⋅A−2
From 1948[5] to 2019, μ0 had a defined value (according to the former definition of the SI amp), equal to:[6][7]
μ0= 4π×10−7\u00A0H/m= 1.25663706143...×10−6\u00A0N/A2(1 henry per meter = 1 newton per square ampere = 1 tesla meter per ampere)
The deviation of the recommended measured value from the previously defined value is statistically significant, at about 3.6σ, reported as μ0/(4π×10
−7\u00A0N⋅A−2)\u00A0−\u00A01 = (5.5±1.5)×10−10. [4]
The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872.[8] The modern notation of permeability as μ and permittivity as ε has been used since the 1950s.
⦁ Role of the magnetic constant in magnetic interaction theory
The magnetic constant plays an important role in the theory of magnetic interactions because it determines how strong an electric current induces a magnetic field and how strong a magnetic field induces an electric current. It thus links mechanical and electromagnetic quantities with each other.
An example of a magnetic interaction that depends on the magnetic constant is unipolar induction, the phenomenon in which a conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field creates a potential difference between the center and the edge with an electrical polarity that depends on the direction of rotation and the orientation of the field. The formula for unipolar inductance is:
$$V = -\frac{d\Phi}{dt} = -\frac{d}{dt}(B_{tot}A\cos{\theta}) = -B_{tot}A\omega\sin{ (\omega t +
\phi)}$$
Where $V$ is the induced voltage, $\Phi$ is the magnetic flux through the disc or cylinder, $B_{tot}
$ is the total magnetic field, $A$ is the area of the disc or cylinder, $\theta $ is the angle between the magnetic field and the normal to the disc or cylinder, $\omega$ is the angular velocity of the disc or cylinder, and $\phi$ is the phase angle of the disc or cylinder.
In this formula, we see that the induced voltage is proportional to the product of the magnetic field and the area, which means that it depends on the magnetic constant. The greater the magnetic constant, the greater the magnetic field induced by an electric current, and the greater the voltage induced by a magnetic field.
Another example of a magnetic interaction that depends on the magnetic constant is Lorentz force, the phenomenon in which a force is exerted on an electrically charged particle moving in a magnetic field. The formula for Lorentz force is:
F=q(v→×B→)
Where $F$ is the Lorentz force, $q$ is the electrical charge of the particle, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field.
In this formula, we see that the Lorentz force is proportional to the product of the magnetic field and the velocity, which means that it also depends on the magnetic constant. The bigger
the magnetic constant, the greater the magnetic field generated by an electric current, and the greater the force exerted on a charged particle.
⦁ Experimental determination and measurements of the magnetic constant
To determine and measure the magnetic constant experimentally, several methods are possible. A common method is based on measuring the inductance of a coil or a solenoid. The formula for the inductance of a coil or a solenoid is:
L=μ0N2Al
Where $L$ is the inductance, $N$ is the number of turns, $A$ is the cross-sectional area, and
$l$ is the length.
In this formula, we see that the inductance is proportional to the magnetic constant. Thus, if we can measure or control the other parameters, we can calculate the magnetic constant from the inductance. This can be done, for example, by running an alternating current through the coil or solenoid and then measuring the voltage and current with an oscilloscope. The inductance can then be found from the relationship between voltage and current in an alternating current circuit:
V=LdIdt
Another method of determining and measuring the magnetic constant is based on measuring the magnetic field generated by a current-carrying wire. The formula for the magnetic field around a current-carrying wire is:
B=μ0I2πr
Where $B$ is the magnetic field, $I$ is the current strength, and $r$ is the distance from the center of
the thread is.
In this formula we see that the magnetic field is proportional to both the current strength and the magnetic constant. So if we can control the current and the magnetic field
can measure at different distances from the wire, we can calculate the magnetic constant from the relationship between magnetic field and distance. This can be done, for example
⦁ Relationship between the magnetic constant and other physical constants
The magnetic constant is an important quantity not only for the description of magnetic interactions, but also for the relationship between other physical constants. An example of this is the fine structure constant, a dimensionless quantity that determines the strength of the electromagnetic interaction between charged particles. The
fine structure constant is defined as:
α=e24πϵ0ℏc
Where $e$ is the elementary charge, $\epsilon_0$ is the electric field constant or the permittivity of the vacuum, $\hbar$ is the reduced Planck constant, and $c$ is the speed of light in vacuum.
In this formula we see that the fine structure constant is proportional to the square of the elementary charge and inversely proportional to the product of the electric field constant, the reduced Planck constant and the speed of light. However, if we use the relationship between the electric field constant and the magnetic constant, which is given by:
c=1ϵ0μ0
Where $c$ is the speed of light in a vacuum, we can rewrite the fine structure constant as:
α=e2μ0c2h
Where $h$ is the Planck constant.
In this formula we see that the fine structure constant is proportional to both the product of the elementary charge and the magnetic constant as with the speed of light, and vice versa proportional to the Planck constant. This means that if we have one of these constants
can measure or determine, we can also calculate the others from the fine structure constant.
Another example of a relationship between the magnetic constant and another physical one constants is the impedance of the vacuum, a quantity that is the relationship between describes electric and magnetic fields in electromagnetic waves. The impedance
of the vacuum is defined as:
Z0=EH=μ0ϵ0
Where $Z_0$ is the impedance of the vacuum, $E$ is the electric field strength, $H$ is the
is magnetic field strength, $\mu_0$ is the magnetic constant, and $\epsilon_0$ is the electrical
field constant.
In this formula, we see that the impedance of the vacuum is proportional to the square root of the ratio between the magnetic constant and the electric field constant. If we however, use the same relationship between these two constants and the speed of light as above, we can rewrite the impedance of the vacuum as:
Z0=μ0c
Where $Z_0$ is the impedance of the vacuum, $\mu_0$ is the magnetic constant, and $c$ is the
speed of light in vacuum.
In this formula, we see that the impedance of the vacuum is proportional to both the magnetic constant as with the speed of light. This means that if we have one of these measure or determine constants, we can also calculate the others from the impedance of the vacuum.
These are just two examples of how the magnetic constant is related to others physical constants. Many other relationships are possible, which testify to the fundamental role that the magnetic constant plays in physics.
OK, I'll try to describe three more relationships between the magnetic constant and other physical constants. Here are some possible examples:
An example of a relationship between the magnetic constant and other physical constants is the magnetic flux quantum, a quantity that describes the minimum magnetic flux difference between two states of a superconducting ring. The magnetic flux quantum is defined as:
Φ0=h2e
Where $\Phi_0$ is the magnetic flux quantum, $h$ is the Planck constant, and $e$ is the elementary charge.
In this formula we see that the magnetic flux quantum is proportional to the Planck constant and inversely proportional to the elementary charge. However, if we use the relation between the elementary charge and the magnetic constant, which is given by:
e=4παℏcμ0
Where $e$ is the elementary charge, $\alpha$ is the fine structure constant, $\hbar$ is the reduced Planck constant, $c$ is the speed of light in vacuum, and $\mu_0$ is the magnetic constant, we can get the magnetic flux quantum rewrite as:
Φ0=παℏcℏcμ0
Where $\Phi_0$ is the magnetic flux quantum, $\alpha$ is the fine structure constant, $
\hbar$ is the reduced Planck constant, $c$ is the speed of light in vacuum, and $\mu_0$ is the magnetic constant.
In this formula we see that the magnetic flux quantum is proportional both to the product of the reduced Planck constant and the square root of the quotient of the reduced Planck constant and the magnetic constant and to the inverse of the fine structure constant and the speed of light. This means that if we can measure or determine one of these constants, we can also calculate the others from the magnetic flux quantum.
Another example of a relationship between the magnetic constant and other physical constants is the Josephson constant, a quantity that describes the relationship between voltage and frequency in a Josephson junction. A Josephson junction is a superconducting device consisting of two superconductors separated by a thin insulator or non- superconducting metal layer. The Josephson constant is defined as:
KJ=2eh
Where $K_J$ is the Josephson constant, $e$ is the elementary charge, and $h$ is the Planck constant.
In this formula we see that the Josephson constant is proportional to the elementary charge and inversely proportional to the Planck constant. However, using the same relationship between the elementary charge and the magnetic constant as above, we can rewrite the Josephson constant as:
KJ=2παμ0ℏc
Where $K_J$ is the Josephson constant, $\alpha$ is the fine structure constant, $\mu_0$ is the magnetic constant, $\hbar$ is the reduced Planck constant, and $c$ is the speed of light in vacuum.
In this formula, we see that the Josephson constant is proportional to both
the fine structure constant as with the square root of the product of the magnetic constant and the reciprocal of the product of the reduced Planck constant and the speed of light. This means that if we can measure or determine one of these constants, we can also measure the others can calculate from the Josephson constant.
A third example of a relationship between the magnetic constant and another physical one constants is the Bohr magneton, a quantity that represents the magnetic moment of a describes electron. The magnetic moment of an electron is due to its spin and
orbital motion around the core. The Bohr magneton is defined as:
μB=eℏ2me
Where $\mu_B$ is the Bohr magneton, $e$ is the elementary charge, $\hbar$ is the reduced
planck constant, and $m_e$ is the mass of the electron.
In this formula, we see that the Bohr magneton is proportional to both the elementary charge as with the reduced Planck constant, and inversely proportional to the mass of it electron. However, if we use the relation between the mass of the electron and
the magnetic constant, which is given by:
ĉme=e24πϵ0ĉ2α
Where $m_e$ is the mass of the electron, $e$ is the elementary charge, $\epsilon_0$ is the electric field constant or the permittivity of the vacuum, $c$ is the speed of light in vacuum is, and $\alpha$ is the fine structure constant, we can rewrite the Bohr magneton as:
μB=2παℏcμ0
Where $\mu_B$ is the Bohr magneton, $\alpha$ is the fine structure constant, $\hbar$ is the reduced
is the planck constant, $c$ is the speed of light in vacuum, and $\mu_0$ is the magnetic constant.
In this formula, we see that the Bohr magneton is proportional to both
the fine structure constant as with the square root of the quotient of the product of it reduced Planck constant and the speed of light and the magnetic constant. This means that if we can measure or determine one of these constants, we can also measure the others calculate from the Bohr magneton.
These are three more examples of how the magnetic constant is related to others physical constants. Many other relationships are possible, which testify to the fundamental role that the magnetic constant plays in physics.
⦁ Experimental Methods and Results
⦁ Design and execution of experiments:
One possible way to write about the experimental confirmation and measurements of the magnetic effect and the applications and implications of the magnetic effect is as follows:
Experimental confirmation and measurements of the magnetic effect
To confirm and measure the magnetic effect of the unipolar dynamo in the center of the hollow Earth, we designed and built an experimental device consisting of the following parts:
⦁ A hollow metal sphere with a diameter of 1 m, representing the hollow earth.
⦁ A permanent magnet with a diameter of 10 cm, representing the unipolar dynamo.
⦁ A shaft that connects the magnet to an electric motor, which controls the rotation of the magnet.
⦁ A conductive disk with a diameter of 20 cm, representing a piece of the inner wall of the hollow earth.
⦁ A shaft that connects the disc to an electric motor, which controls the rotation of the disc.
⦁ A voltmeter that measures the potential difference between the center and the edge of the disc.
⦁ An ammeter that measures the electric current through the disc.
⦁ A hall probe that measures the magnetic field at various points in the hollow sphere.
We placed the device in a vacuum chamber to avoid air resistance and eddy currents. We performed several experiments by varying the rotational speeds of the magnet and the disc and by changing the position of the Hall probe. We obtained the following results:
⦁ A potential difference and an electric current were induced in the disc, which depended on the rotational speed of the magnet, the magnetic field of the magnet, the surface of the disc, and the angle between the magnetic field and the normal to the disc . The values were consistent with the formula for unipolar inductance.
⦁ A magnetic field was generated by the electric current in the disc, which depended on the current strength, the surface of the disc, and the distance from the center of the disc. The magnetic field was directed radially and had the same polarity all over the disk. The values matched the formula for the magnetic field of a unipolar dynamo.
⦁ A Lorentz force was exerted on a small metal ball that we placed in the hollow sphere, which depended on the charge, the speed and the magnetic field of the ball. The Lorentz force pushed the ball to the edge of the hollow sphere, causing it to follow a circular trajectory in a plane perpendicular to the magnetic field. The radius of the circle
depended on the mass, speed, charge and magnetic field of the ball. The values were consistent with the formula for Lorentz force.
These results thus confirm the existence and properties of the magnetic effect of the unipolar dynamo in the center of the hollow earth.
Applications and implications of the magnetic effect
The magnetic effect of the unipolar dynamo at the center of the hollow Earth has several applications and implications for the life and culture of
the people who live in the hollow earth. Some examples are:
⦁ The magnetic effect can be used as a source of electrical energy, tapping the induced voltage and current in the disc or cylinder and using it for various purposes, such as lighting, heating, communication, etc.
⦁ The magnetic effect can be used as a means of transportation, using the Lorentz force to move vehicles or objects along the inner wall of the hollow earth, without contact or friction.
⦁ The magnetic effect can be used as an art form, by manipulating the light and heat effects produced by the unipolar dynamo and combining them with other elements, such as colors, sounds, shapes, etc.
⦁ The magnetic effect also has implications for the science, philosophy, religion, and ethics of the people who inhabit the hollow earth, as it confronts them with fundamental questions about the nature and origin of the universe, its role and meaning of life, the limits and responsibilities of knowledge, etc.
In this chapter I describe and justify the methods I used to answer my research question: How does the unipolar dynamo work in a hollow Earth? My research is based on an experimental approach, using a homopolar generator to measure the induced voltage in a unipolar alternator and compare it with the predictions of the Folgers formula. I explain how I designed and built the homopolar generator, what tools and techniques I used to
measure the voltage and magnetic field, how I collected and analyzed the data, what ethical issues I considered, and what limitations there were to my research.
A homopolar generator is a device that generates electrical current by rotating a conductive disc in a magnetic field. It is a simple example of a unipolar dynamo, where there is no relative motion between the magnetic field and the disc. In magnetic system B, where the Earth is a hollow ball with a unipolar dynamo in the center, we built a homopolar generator to study the induced voltage phenomenon. We did this because we could always see a very wonderful scene when we observed tension when there was no relative motion. Quite a force that no one could name or seize. Chris Folgers, the lead researcher of this project, by building the same homopolar generator but now with his formula in hand,
The Folgers formula is a mathematical expression that describes the induced voltage in a unipolar alternator as a function of the total magnetic field, the area of the disc, the angular velocity and the phase angle. The formula is as follows:
$$V = -\frac{d\Phi}{dt} = -\frac{d}{dt}(B_{tot}A\cos{\theta}) = -B_{tot}A\omega\sin{ (\omega t +
\phi)}$$
Where $V$ is the induced voltage, $\Phi$ is the magnetic flux through the disc, $B_{tot}$ is the total magnetic field, $A$ is the area of the disc, $\theta$ is the angle between is the magnetic field and the normal to the disk, $\omega$ is the angular velocity of the disk, and $\phi$ is the phase angle of the disk.
The aim of our experiment was to test whether the Folgers formula corresponds to reality in magnetic system B. We also wanted to investigate how the magnetic field varies in different parts of the hollow Earth and the implications of using a unipolar dynamo as an energy source.
In the following sections I describe in detail how we conducted our experiment and what results we obtained.
One possible way to explain the physical principles behind the unipolar dynamo is as follows:
A unipolar dynamo is a type of direct current generator consisting of a conductive disc or cylinder rotating in a plane perpendicular to a uniform static magnetic field. Between the center of the disc or cylinder and the rim, a potential difference is created with an electrical polarity that depends on the direction of rotation and the orientation of the field. ¹
A unipolar alternator works on the principle of electromagnetic induction, which states that an electric current is generated in a closed circuit when the magnetic flux through that circuit changes. The magnetic flux is the product of the magnetic field and the surface perpendicular to that field. As the disc or cylinder rotates, the angle between the magnetic field and the normal to the disc or cylinder changes, causing the magnetic flux to vary. This causes an induced voltage that is proportional to the rate of change of the flux. ³
Another way to understand the principle of a unipolar dynamo is to use the Lorentz force, which states that the force on an electrically charged particle is proportional to the vector product of its velocity and the magnetic field. When the disc or cylinder rotates, the electrons in the conductive material also move at a certain speed. These electrons then experience a Lorentz force perpendicular to both their velocity and the magnetic field.
This force pushes the electrons to the edge of the disc or cylinder, creating a negative charge at the edge and a positive charge at the center. This creates a potential difference that is proportional to the product of the velocity, magnetic field, and radius of the disc or cylinder.
The unipolar dynamo is unique in that there is no relative motion between the magnetic field and the disc or cylinder. This means that no commutator or slip rings are required to convert the alternating voltage to DC voltage, as is the case with other types of alternators. The unipolar alternator can also generate very strong currents because it can have very low internal resistance.
In a hollow Earth, the magnetic field is created by a unipolar dynamo in the center of the hollow sphere. This is a conductive disc or cylinder that rotates in a plane perpendicular to a uniform static magnetic field. This magnetic field can come from a permanent magnet or from an electric current flowing through the disc or cylinder1
The rotation of the unipolar dynamo creates a potential difference between the center and the edge of the disc or cylinder, causing an electric current to flow. This current, in turn, generates a magnetic field perpendicular to the plane of the disc or cylinder. This magnetic field is thus directed radially and has the same polarity over the entire disc or cylinder1
The magnetic field of the unipolar dynamo extends to the inner wall of the hollow Earth, to which it is perpendicular. The magnetic field is strongest near the hollow Earth's equator, where it is parallel to the surface, and weakest near the poles, where it is perpendicular to the surface. The magnetic field decreases with distance from the unipolar dynamo according to Gauss's law of magnetism2
The magnetic field of the unipolar dynamo affects the life and culture of the people living in the hollow earth. For example, it creates an artificial day and night cycle, because the light emitted by the dynamo varies with the rotation. It also creates an artificial climate, as it generates heat through the electrical resistance of the disc or cylinder. Finally, it creates an artificial gravity, because it exerts a Lorentz force on the electrically charged particles in the air and in people's bodies
A possible way to put the mathematical formulas together is as follows: The induced voltage in a unipolar alternator is given by the formula:
$$V = -\frac{d\Phi}{dt} = -\frac{d}{dt}(B_{tot}A\cos{\theta}) = -B_{tot}A\omega\sin{ (\omega t +
\phi)}$$
Where $V$ is the induced voltage, $\Phi$ is the magnetic flux through the disc or cylinder, $B_{tot}
$ is the total magnetic field, $A$ is the area of the disc or cylinder, $\theta $ is the angle between the magnetic field and the normal to the disc or cylinder, $\omega$ is the angular velocity of the disc or cylinder, and $\phi$ is the phase angle of the disc or cylinder.
The electric current in a unipolar alternator is given by the formula:
I=VR=−BtotAωRsin(ωt+ϕ)
Where $I$ is the electric current, $R$ is the total resistance of the disc or cylinder and the external circuit.
The magnetic field generated by a unipolar dynamo is given by the formula:
B=μ0Ir2R2
Where $B$ is the magnetic field, $\mu_0$ is the magnetic permeability of the vacuum, $r$ is the radius of the disc or cylinder, and $R$ is the distance from the center of the disc or cylinder.
The Lorentz force exerted by a unipolar dynamo on an electrically charged particle is given by the formula:
F=q(v→×B→)
Where $F$ is the Lorentz force, $q$ is the electrical charge of the particle, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field.
⦁ The interaction between the magnetic field of the unipolar dynamo in the center of the hollow earth and the conductive disc or cylinder that generates the field. This interaction creates an electromagnetic induction that generates a potential difference and an electric current in the disc or cylinder. ¹
⦁ The interaction between the magnetic field of the unipolar dynamo and the electrically charged particles in the air and in the bodies of the people living in the hollow earth.
This interaction creates a Lorentz force that pushes the particles to the edge of the hollow Earth, creating an artificial gravity. ¹
⦁ The interaction between the magnetic field of the unipolar dynamo and the magnetic field of the solar wind, a stream of charged particles emanating from the sun. This interaction creates a magnetosphere, a protective layer that shields the hollow Earth from harmful cosmic rays. ²
These magnetic interactions have different consequences for the lives and culture of the people who inhabit the hollow earth. For example, they determine their day and night cycle, their climate, their energy source, their communication, their navigation and their health. ³
A possible way to give the relevant formulas for the possible magnetic interactions in magnetic system B is as follows:
The formula for the induced voltage in a unipolar alternator is:
$$V = -\frac{d\Phi}{dt} = -\frac{d}{dt}(B_{tot}A\cos{\theta}) = -B_{tot}A\omega\sin{ (\omega t +
\phi)}$$
Where $V$ is the induced voltage, $\Phi$ is the magnetic flux through the disc or cylinder, $B_{tot}
$ is the total magnetic field, $A$ is the area of the disc or cylinder, $\theta $ is the angle between the magnetic field and the normal to the disc or cylinder, $\omega$ is the angular velocity of the disc or cylinder, and $\phi$ is the phase angle of the disc or cylinder.
The formula for the Lorentz force on an electrically charged particle in a magnetic field is:
F=q(v→×B→)
Where $F$ is the Lorentz force, $q$ is the electrical charge of the particle, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field.
The formula for the magnetosphere of a hollow Earth in a solar wind is:
Psw=Pmf
Where $P_{sw}$ is the pressure of the solar wind, $P_{mf}$ is the pressure of the magnetic field of the unipolar dynamo.
OK, I'll try to explain both cases.
An electrically charged particle experiencing a magnetic field experiences a Lorentz force perpendicular to both its velocity and the magnetic field. The formula for the Lorentz force is:
F=q(v→×B→)
Where $F$ is the Lorentz force, $q$ is the electrical charge of the particle, $\vec{v}$ is the velocity of the particle, and $\vec{B}$ is the magnetic field.
If the particle moves in a uniform magnetic field, it will follow a circular path in a plane perpendicular to the magnetic field. The radius of the circle is given by:
r=mvqB
Where $m$ is the mass of the particle.
A magnetic dipole moment that experiences a magnetic field experiences a magnetic force and a magnetic torque that depend on the angle between the dipole moment and the magnetic field. The formula for the magnetic force is:
F=(m→⋅∇)B→
Where $F$ is the magnetic force, $\vec{m}$ is the magnetic dipole moment, $\nabla$ is the nabla operator, and $\vec{B}$ is the magnetic field.
The formula for the magnetic torque is:
τ=m→×B→
Where $\tau$ is the magnetic torque.
If the dipole moment is in a uniform magnetic field, it will not experience any magnetic force, but it will experience a magnetic torque that will spin the dipole moment until it is parallel to the magnetic field. The size of the torque is given by:
τ=mBsinθ
Where $\theta$ is the angle between the dipole moment and the magnetic field.
Chapter 8. Interaction of Magnetism with Other Particles and Forces
In this chapter we will examine how magnetism interacts with other particles and forces in nature. We will see how magnetic interaction theory explains and predicts these interactions, and what connections and implications there are for our understanding of physics.
⦁ Magnetic interaction and electric currents
An electric current is a movement of electrically charged particles, such as electrons or ions. An electric current can generate a magnetic field perpendicular to the direction of the current. This is called the electromagnetic induction phenomenon. Conversely, a changing magnetic field can also induce an electric current in a conductor, which is perpendicular to the direction of the field. This is called the electromagnetic induction phenomenon.
The magnetic interaction theory explains these phenomena by assuming that a magnetic particle exists, which has both an electric charge and a magnetic moment. The magnetic moment is a vector that indicates the strength and direction of the magnetic field. The magnetic particle can interact with both the local and global magnetic field, causing an induced voltage in a conductor. The induced voltage is equal to the negative of the time derivative of the magnetic flux through the disc. The magnetic flux is equal to the product of the total
magnetic field and the surface of the disk and the cosine of the angle between the magnetic field and the normal to the disk. The total magnetic field is equal to the sum of the local and global fields. The angle changes as the disc rotates with an angular velocity and a phase angle.
This formula is called the Folgers formula for the induced voltage in a unipolar alternator. A unipolar dynamo is a device that generates electricity by using a rotating disc in a magnetic field. The Folgers formula predicts that the induced voltage depends on both the local and global magnetic field, and can vary according to the disk's rotation and phase.
⦁ Magnetic interaction and electromagnetic radiation
Electromagnetic radiation is a form of energy consisting of oscillating electric and magnetic fields that propagate through space at a constant speed. Electromagnetic radiation can have different frequencies and wavelengths, which together form the electromagnetic spectrum. Examples of electromagnetic radiation are light, radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays and gamma rays.
The magnetic interaction theory explains how electromagnetic radiation is produced and influenced by magnetism. According to this theory, an accelerating or oscillating magnetic particle can emit or absorb electromagnetic radiation depending on its frequency and phase relative to the local or global magnetic field. The energy and angular momentum of the magnetic particle then change according to the law of conservation of energy and angular momentum.
Magnetic interaction theory predicts that the intensity and polarization of the electromagnetic radiation depend on the magnetic constant, which is a measure of the strength of the magnetic interaction. The magnetic constant is a fundamental physical constant that can be determined and measured experimentally. The magnetic constant is related to other physical constants, such as the speed of light, the electrical constant, the magnetic permeability, and the magnetic susceptibility.
⦁ Magnetic interaction and gravity
Gravity is a fundamental force of nature, which causes the attraction between masses. Gravity is responsible for the movement of celestial bodies, such as
planets, stars and galaxies. Gravity is described by general relativity, which states that gravity results from the curvature of space and time due to mass and energy.
The magnetic interaction theory explains how magnetism interacts with gravity. According to this theory, a magnetic particle can have both a mass and an energy, which depend on its electrical charge and its magnetic moment. The magnetic particle can therefore be both a source and a receiver of gravity. The magnetic particle can also warp space and time through its mass and energy, creating a gravitomagnetic field. A gravitomagnetic field is an analog of the electromagnetic field, but for gravity.
Magnetic interaction theory predicts that the gravitomagnetic field depends on both the local and global magnetic field, and that it can vary according to the rotation and phase of the magnetic particle. The gravitomagnetic field can affect the motion and trajectory of other masses and energies nearby. The gravitomagnetic field can also interfere with the electromagnetic field, causing new phenomena such as gravitomagnetic waves.
⦁ Magnetic interaction and nuclear forces
Nuclear forces are fundamental forces of nature, which determine the interactions between subatomic particles, such as protons and neutrons. Nuclear forces are responsible for the stability and structure of atoms and nuclei. Nuclear forces are described by two theories: the strong nuclear force and the weak nuclear force. The strong nuclear force holds protons and neutrons together in nuclei, while the weak nuclear force is involved in radioactive decay.
The magnetic interaction theory explains how magnetism interacts with nuclear forces. According to this theory, a magnetic particle can have both a colored charge and a weak charge, which depend on its electric charge and its magnetic moment. The magnetic particle can thus be both a source and a receiver of nuclear forces. The magnetic particle can also interact with other subatomic particles, such as quarks and leptons, which also have colored or weak charges.
Magnetic interaction theory predicts that the strength and range of the nuclear forces depend on both the local and global magnetic field, and that they can vary according to the rotation and phase of the magnetic particle. The magnetic particle can also influence the bonding and decay of atoms and nuclei, thus causing new phenomena such as magnetic isotopes, magnetic resonance or magnetic fusion.
⦁ Relationships and implications of magnetic interaction theory
In this chapter we have seen how magnetism interacts with other particles and forces in nature. We have seen how magnetic interaction theory explains and predicts various aspects of physics, and what connections and implications there are for our understanding of reality. The magnetic interaction theory states that a magnetic particle exists, which has both an electric charge and a magnetic moment, and can interact with both the local and the global magnetic field. The magnetic particle can also interact with other particles and forces, such as electric currents, electromagnetic radiation, gravity and nuclear forces. The magnetic interaction theory is based on the Folgers formula for the induced voltage in a unipolar alternator, which depends on both the local and global magnetic field, and which can vary according to the rotation and phase of the disk. The magnetic interaction theory also relies on the magnetic constant, which is a measure of the strength of the magnetic interaction, and which has a relationship with other physical constants.
The magnetic interaction theory has several connections and implications for our understanding of reality. First, it offers a new way of looking at magnetism, not as a derivative or a by-product of electricity or relativity, but as a fundamental and independent force of nature. Second, it offers a new way of looking at the unipolar dynamo, not as a simple or trivial device, but as a complex and fascinating phenomenon. Third, it offers a new way of looking at the universe, not as a static or deterministic whole, but as a dynamic and probabilistic system.
However, magnetic interaction theory is not without challenges and limitations. First, it is still a hypothetical and speculative theory, needing more experimental confirmation and theoretical refinement. Second, it is still an incomplete and partial theory, which cannot explain or predict all aspects of physics. Third, it is still a controversial and alternative theory, not widely accepted or recognized by the scientific community.
In this thesis we have tried to present and substantiate the magnetic interaction theory with arguments and evidence. We also tried to inform and inspire the reader with our vision and our passion. We hope that we have succeeded, and that we have contributed to the advancement of knowledge and science.
Chapter 9. Conclusion
In this thesis, we proposed and investigated a new theory, which we named the magnetic interaction theory. The magnetic interaction theory is one
theory that attempts to explain and predict magnetism as a fundamental and independent force of nature, interacting with other particles and forces in nature. The magnetic interaction theory is based on the existence of a magnetic particle, which has both an electric charge and a magnetic moment, and can interact with both the local and the global magnetic field. Magnetic interaction theory also relies on the Folgers formula for the induced voltage in a unipolar dynamo, which depends on both the local and global magnetic field, and can vary according to the rotation and phase of the disk. The magnetic interaction theory also relies on the magnetic constant, which is a measure of the strength of the magnetic interaction,
In this thesis, we asked and answered the following research questions:
⦁ What are the foundations and concepts of the magnetic interaction theory?
⦁ How does the magnetic interaction theory explain and predict magnetic interaction inside and outside a unipolar dynamo?
⦁ What are the properties and behavior of the magnetic particle?
⦁ What is the magnetic effect and how is it caused and measured?
⦁ What is the magnetic constant and how is it determined and measured?
⦁ How does magnetism interact with other particles and forces in nature, such as electric currents, electromagnetic radiation, gravity and nuclear forces?
⦁ What are the connections and implications of the magnetic interaction theory for our understanding of reality?
We have answered these research questions using various methods, such as literature review, theoretical analysis, experimental design and implementation, data collection and analysis, presentation and interpretation of results, comparison with existing theories and models, and argumentation and evidence.
We have drawn several results and conclusions from our research, such as:
⦁ The magnetic interaction theory is a new and original theory, which offers a new way of looking at magnetism.
⦁ The magnetic interaction theory is a realistic and plausible theory, which is consistent with observations and experiments.
⦁ The magnetic interaction theory is a complex and detailed theory that explains and predicts many aspects of physics.
⦁ The magnetic interaction theory is a hypothetical and speculative theory, which needs more experimental confirmation and theoretical refinement.
⦁ The magnetic interaction theory is an incomplete and partial theory, which cannot explain or predict all aspects of physics.
ADDITIONAL APPENDICES and explanations:
The Folgers formula is a mathematical expression that tells us how much voltage is generated in a unipolar alternator. This voltage depends on several factors, namely the total magnetic field, the area of the disk, the angular velocity and the phase angle. The formula looks like this:
To calculate the induced voltage (V), we need to determine the magnetic flux (Φ) through the disc. We do this by combining the total magnetic field (Btot), the area of the disk (A), and the angle (θ) between the magnetic field and the normal to the disk. Then we take the negative derivative of this value with respect to time (t). Finally we get:
V equals minus the derivative of Φ with respect to t, or minus the derivative of (Btot * A * cos(θ)) with respect to t, which is minus Btot * A * angular velocity * sine(angular velocity * time + phase angle).
Thus, the induced voltage (V) depends on the total magnetic field, the area of the disc, the angular velocity and the phase angle. This formula helps us understand the voltage in a unipolar alternator.
In addition, we have another formula that describes the electric current (I) in a unipolar alternator. This is determined by the induced voltage (V) and the total resistance of the disc or cylinder (R). The formula is as follows:
To calculate the electric current (I), we divide the induced voltage (V) by the total resistance (R). This gives us:
I equals V divided by R, which means minus Btot * A * angular velocity * sine(angular velocity
* time + phase angle) divided by R.
This is how we can determine the electric current in a unipolar alternator taking into account the induced voltage and the total resistance.
Briefly, the Folgers formula describes the induced voltage and the electric current in a unipolar dynamo, where the induced voltage depends on the total magnetic field, the area of the disc or cylinder, the angular velocity and the phase angle.
The Lorentz force on an electrically charged particle in a magnetic field is given by the formula:
The force (F) acting on the particle is equal to the particle's charge (q) multiplied by the cross product of the particle's velocity (v) and the magnetic field (B).
The magnetosphere of a hollow Earth in a solar wind is described by the formula:
The pressure (Psw) of the solar wind is equal to the pressure (Pmf) of the magnetic field of the unipolar dynamo.
For magnetic particles on Earth we have the following formulas:
An electrically charged particle experiencing a magnetic field experiences a Lorentz force that is perpendicular to both the velocity and the magnetic field. The formula for the Lorentz force is:
The force (F) acting on the particle is equal to the particle's charge (q) multiplied by the cross product of the particle's velocity (v) and the magnetic field (B).
If the particle moves in a uniform magnetic field, it will follow a circular path in a plane perpendicular to the magnetic field. The radius (r) of the circle is given by:
The radius (r) of the circle in which the particle moves is equal to the charge (q) of the particle multiplied by the magnetic field (B), the mass (m) of the particle, and the velocity (v) of the particle .
A magnetic dipole moment that experiences a magnetic field experiences a magnetic force and a magnetic torque that depend on the angle between the dipole moment and the magnetic field. The formula for the magnetic force is:
The force (F) acting on the magnetic dipole moment is equal to the cross product of the magnetic dipole moment (m) and the gradient (nabla operator,∇)of the magnetic field (B).
The formula for the magnetic torque is:
The torque (τ) acting on the magnetic dipole moment is equal to the cross product of the magnetic dipole moment (m) and the magnetic field (B).
If the dipole moment is in a uniform magnetic field, it experiences no magnetic force, but it does experience a magnetic torque that rotates the dipole moment until it is parallel to the magnetic field. The magnitude of the torque is given by:
The torque (τ) acting on the magnetic dipole moment is equal to the product of the magnetic dipole moment (m), the magnetic field (B
The induced voltage (V) is equal to the change of magnetic flux (Φ) through the disc or cylinder per unit time. This is also equal to the product of the total magnetic field (Btot), the area (A) of the disc or cylinder, the angular velocity (ω) of the disc or cylinder, and the sine of the sum of the angular velocity (ω) multiplied by the time (t) plus the phase angle (ϕ).
An example of a magnetic interaction that depends on the magnetic constant is the Lorentz force. This is the force (F) exerted on an electrically charged particle moving in a magnetic field. The force (F) is equal to the particle's charge (q) multiplied by the cross product of the particle's velocity (v) and the magnetic field (B).
To determine and measure the magnetic constant experimentally, several methods are possible. A common method is based on measuring the inductance of a coil or a solenoid. The inductance (L) of the coil or solenoid is proportional to the magnetic constant (µ0), the number of turns (N), the cross-sectional area (A), and the length (l) of the coil or solenoid.
Another method of determining and measuring the magnetic constant is based on measuring the magnetic field generated by a current-carrying wire. The magnetic field (B) around the wire is proportional to the magnetic constant (µ0), the current (I) and the distance (r) from the center of the wire.
By performing experiments that measure the inductance of coils or solenoids or measure the magnetic field around current-carrying wires, we can calculate and determine the magnetic constant.
The relationship between the magnetic constant and other physical constants can be seen in several formulas. For example, the fine structure constant, which describes the electromagnetic interaction between charged particles, is proportional to the product of the elementary charge and the magnetic constant, and inversely proportional to the speed of light and the Planck constant.
This can be rewritten using the relationship between the electric field constant, the magnetic constant and the speed of light.
Another example is the impedance of the vacuum, which describes the relationship between electric and magnetic fields in electromagnetic waves. The impedance of the vacuum is proportional to the magnetic constant and the speed of light. Again, the relationship between the magnetic constant and the speed of light can be used to calculate the impedance.
These relationships between the magnetic constant and other physical constants show how these quantities are linked in fundamental physical phenomena. By means of
By measuring or determining one of these constants, we can calculate other constants and gain a deeper understanding of the underlying principles of nature.
You pronounce the formula like this:
The integral of the dot product of the magnetic field B and the infinitesimal length element dl, taken over the closed curve, is equal to the magnetic constant μ0 multiplied by the double integral of the dot product of the current density J and the infinitesimal area element dS, plus the time derivative of the double integral of the dot product of the electric field E and the infinitesimal surface element dS.
The integral of the dot product of the electric field E and the infinitesimal length element dl, taken over the closed curve, is equal to the negative time derivative of the double integral of the dot product of the magnetic field B and the infinitesimal area element dS.
In simpler terms, this formula describes how the electric field and the magnetic field are related. It shows that the circulation of the electric field along a closed curve is proportional to the negative change of the magnetic field through the spanned surface. It thus describes the relationship between electromagnetic fields and how they influence each other over time.
The double integral of the dot product of the magnetic field B and the infinitesimal surface element dS equals zero.
In simpler terms, this formula describes Gauss's law for magnetism. It says that the total flux of the magnetic field through a closed surface is always zero. In other words, there are no isolated sources or sinks of magnetic field (no magnetic monopoles). The magnetic field always has closed lines that have no beginning or end.
The fine structure constant α is equal to 4πϵ0ℏce2.
where e is the elementary charge, ϵ0 is the electric field constant (or permittivity of the vacuum),ℏthe reduced Planck constant and c the speed of light in vacuum.
The second formula is pronounced as follows:
The speed of light in vacuum c is equal to the product of ϵ0 and μ0 (the magnetic constant) with the value 1.
In addition, we can rewrite the fine structure constant α as:
α is equal to 2he2μ0c, where h is the Planck constant.
This means that the fine structure constant α is proportional to the product of the square of the elementary charge e, the magnetic constant μ0 and the speed of light in vacuum c, and is inversely proportional to the Planck constant h.
You pronounce the first formula as follows:
The impedance of the vacuum Z0 is equal to the product of the electric field strength E and the magnetic field strength H, which in turn is equal to the product of ϵ0 (electric field constant) and μ0 (magnetic constant).
The second formula is pronounced as follows:
The impedance of the vacuum Z0 is equal to the product of the magnetic constant μ0 and the speed of light in vacuum c.
This means that the impedance of the vacuum Z0 is proportional to both the magnetic constant μ0 and the speed of light in vacuum c.
The Folgers-Pan equation is expressed as follows:
The change of the vector E with respect to time is equal to a function F of E. Here E represents an event vector, t represents time, and F represents the interaction between events.
Faraday's law is pronounced as follows:
The vectorial rotation of the electric field E is equal to minus the change of the magnetic field B with respect to time. Here the operator represents∇× the vectorial rotation and t the time. This equation shows that a changing magnetic field can generate an electric field that revolves around the region where the magnetic field changes. This is also known as electromagnetic induction.
The Ampère-Maxwell law is expressed as follows:
The vector rotation of the magnetic field B is equal to μ0 times the current density J plus μ0 times the permittivity of the vacuum ϵ0 times the change of the electric field E with respect to time.
The equation∇×B equals μ0 times J plus μ0 times ϵ0 times the change of E over time. Hereby stands∇× for the vectorial rotation of B, μ0 for the magnetic constant, J for the current density, ϵ0 for the permittivity of the vacuum, ∂t/∂E for the change of E with respect to time.