Taking the divergence of the Ampere’s Circuital Law give by ▼×H = J and using the continuity equation we have
That is, equation ▼×H = J leads to steady state conditions in which charge density is not time varying function. Therefore, for time dependent fields’ ▼×H = J needs some modifications. Maxwell suggested that the definition of total current density of Ampere’s Circuital Law is incomplete and advised to add something to J. If it is assumed to be J’, we have
Since J’ arises due to the variation of electric displacement (electric flux density) D with time, it is termed as displacement current density. The modified Ampere’s Circuital Law (Maxwell’s equation), therefore, for time varying field takes the following form
The important conclusion that can be drawn now is that, since displacement current is related to the electric field, it is not possible in case of time varying fields to deal separately with electric and magnetic fields but, instead, the two fields are interlinked giving rise to electromagnetic fields. It is to be noted that, in a good conductor J’ is negligible compared to J at frequency lower than light frequencies (1015 Hz).