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# The Maxwell equations that define all phenomena of electromagnetism.

The Maxwell equations can be used to calculate all electrical and magnetic events, such as electrical and magnetic forces. See how the equations are.

## What are the Maxwell equations?

The Maxwell equations represent the most essential operations of electrodynamics. He uses physical theory to describe all the laws of electromagnetism. The equations were named after the inventor James Clerk Maxwell, who invented these equations in 1864. Using these equations, all electrical and magnetic events can be calculated. These include, for example, the electrical and magnetic forces in the existing distributions of current and charge.

## Who was James Clerk Maxwell?

Theoretical magnetism waited a long time for an exact mathematical calculation and description. And in 1864, James Clerk Maxwell described them completely in the physical sense. The equations found by Maxwell form the basis of electrodynamics to this day. The equations describe how large magnetic and electric fields are. As a result, the corresponding forces can be derived. Maxwell also realized that magnetic and electrical events are not independent of each other. A moving electric field also generates magnetic fields.

## How did Maxwell's equations revolutionize magnetism?

Time-varying electric and magnetic fields influence each other in electromagnetic waves. The consideration of electrical polarization, as well as magnetization, is carried out by extending the vacuum equations. As a result, the propagation of magnetic and electric fields in matter can also be described.

The equations use their own mathematical differential operator, which is also called a derivative vector. The symbol of this derivative vector is a triangle at the top: ∇⃗ = ( / x / y / z). X is the partial derivative to / x.

This describes the proportion of field lines E, for example, of an electric field E with the help of the divergence of field V * E. But there are also vortices (loops of field lines) with the possible derivative. These are calculated with the cross product VxE.

The curves of the electric fields and the magnetic flux density are described by time-independent equations. In this case, the currents j and the static charges ρ must be known in vacuum or almost in vacuum.

1) ∇⋅E = ρ / ε 0.

2) × E = 0.

3) ∇⋅B = 0.

4) × B = μ0 j.

ε 0 represents the dielectric constant for vacuum.

Μ0 represents the magnetic permeability of the vacuum.

## The equations allow the following conclusions:

1. Charges generate field lines. Positive charges are the sources of electric fields. Negative charges are the sumps of electric fields. The sources of electric fields are described by their divergence. The strength of an electric field is proportional to the load.
2. At rest, white electric fields without vortex. On the cross product, vortices are calculated.
3. However, the sources are not present in the magnetic flux density. Magnetic monopolies or physical objects emanating from magnetic field lines.
4. The fourth vortex of magnetic flux density and, therefore, magnetic fields are caused by vortex. The force of a magnetic field is proportional to the current included.

Time variable electromagnetism is considered in time dependent equations. The change in the electric field is calculated as E = (d / dt) * E. The equations that vary with time in vacuum are:

1) ∇⋅E = ρ / ε0.

2) × ˙ + B˙ = 0.

3) ∇⋅B = 0 ª

4) × B = μ0j + (1 / c2) * E.

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