MagneticFields

For a special project of mine that will certainly revolution the entire world , I needed to understand basic Electro-Magnetism theory.

This page deals with my encounter and difficulties but also with the results of my research.

Electro-Magnetism

Electro-Magnetism is a huge but absolutely necessary and fundamental domain in physics as it's the basis for most physical phenomena and study fields like optics, radio-astronomy, quantum physics, electronics, particles study, etc.

Electricity and magnetism were first seen as two distinct phenomena until the work of famous scientists like Ampère, Gauss, Faraday or Maxwell actually made the two inter-related. More than inter-related : actually inseparable from one another.

To test my Tex package, I'll list the 4 beautiful Maxwell equations (in stationary regime) that tie electricity and magnetism but also completely define them :

<math>\nabla \times \mathbf{H} = \mathbf{j}</math>	(1)
<math>\nabla \cdot \mathbf{B} = 0</math>	(2)
<math>\nabla \times \mathbf{E} = \mathbf{0}</math>	(3)
<math>\nabla \cdot \mathbf{D} = \rho_e</math>	(4)

where Boldface symbols are vectors, regular symbols are simple scalars and

<math>\mathbf{H}</math> is the magnetic field strength (or magnetic intensity) in <math>A.m^{-1}</math> (Ampère per mètre)

<math>\mathbf{B}</math> is the magnetic flux density (or magnetic induction) in <math>T</math> (Tesla)

<math>\mathbf{D}</math> is the electric flux density (or electric induction) in <math>C.m^{-2}</math> (Coulomb per square mètre)

<math>\mathbf{E}</math> is the electric field strength (or electric intensity) in <math>V.m^{-1}</math> (Volt per mètre)

<math>\mathbf{j}</math> is the free current density (that is, the current density related to the transport of free electric charges) in <math>A.m^{-2}</math> (Ampère per square mètre)

<math>\rho_e</math> is the volume density of free electric charges in <math>C.m^{-3}</math> (Coulomb per cubic mètre)

Notice the beautiful symmetry in these 4 equations. We will mostly leave the electric field equations aside in the following and concentrate on the magnetic field equations.

Typically, equations (1) and (2) simply mean that a magnetic field line always closes back to the emitter and that the net magnetic flux is always 0 as there is always the same amount that goes off of a surface that comes back into it as stated in the following Gauss equation :

<math>\oint_S \mathbf{B} \cdot dA = 0</math> (for a closed surface)

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