Saturday, January 16, 2010

The Significance of Displacement Current

The Ampere’s Circuital Law for static field is no longer useful in time varying fields as is shown below:

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

Applying Stokes’s Theorem in equation (1) can be given in integral form as

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).