Maxwell Electromagnetic Field

The fundamental equations of the electromagnetic field as derived by Maxwell are:



Here is the electric displacement, ρ is the electric charge density, is the magnetic flux density, is the current density and is the electrical intensity. Equation (1) is an important contribution by Maxwell. The term represents the displacement current density. In the absence of this term, equation (1) represents Ampere’s law. Equation (2) represents Maxwell’s generalization Neumann’s law of electromagnetic induction. Equation (3) represents Gauss’s flux law in magnetism.

This establishes the fact that a single magnetic pole cannot exist. Maxwell’s equations relate to mathematical expressions based on certain experimental results. Though it is not possible to prove the equations, yet their applicability to any particular situation can be verified. Maxwell’s equations are now used as guiding principles in a large number of situations.

But from the equation of continuity of charge (equation 3)



i.e. div is zero for steady state only.



This equation will reduce to div J = 0 in the case of steady state.

According to equation (6), the current density, should be written as



However, is the conduction current density and is the displacement current density.

In equation (1), if is omitted, it will be identical with equation (2). It means that a change in magnetic flux induces an electric field and a change in the electric flux induces a magnetic field. However, displacement currents will be significant only at rapidly varying fields i.e. only at high frequencies.

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