Question

What is displacement current? Why was this concept introduced? Explain. Also obtain the Ampere-Maxwell equation.

Answer 1

Displacement current is a quantity appearing in Maxwell’s Equation. It is defined in terms of the rate of change of electric displacement field. The units of displacement current are same as that of electric current density. Displacement current is not an electric current caused due to moving of charges(called conventional current), but it is caused by a time varying electric field.

If we consider a capacitive circuit, we can see there is current flowing through the circuit. But if you look at the capacitor plates, there is a small empty region in between them.

Then how the circuit is completed?

The circuit is completed despite the small space because there is displacement in that region which is developed as a consequence of the electric field in between the plates.
So according to Ampere circuital law,

$\oint \overrightarrow{B}.\overrightarrow{d}l={\mu }_0(I_c+I_D)$

where Ic is conduction current, and Id is displacement current.

Displacement current caused by varing electric field therefore has
$I{}_D={ϵ}_o\frac{d{\varphi }_E}{dt}$

Substituting the value in Ampere circuital law. We get

$\oint \overrightarrow{B}.\overrightarrow{d}l={\mu }_o(I_C+{ϵ}_o\frac{d{\varphi }_E}{dt})$

Hence the ampere Circutal law is modified to Ampere-Maxwell Law.