^Maxwell law

Just as Faraday’s law tells us that a time-varying magnetic field produces an electric field, the Ampere-Maxwell law predicts that a time-varying electric field produces a current & magnetic field.

This current is called Maxwell displacement current.

Let  is the rate of change of electric flux of through the area bounded by the closed curve along which the circulation of  is calculated, then Maxwell -Ampere law is expressed as

Here  is called the displacement current.

Consider a uncharged parallel-plate capacitor connected to a battery through a switch. On closing the switch the charge on capacitor plates increases, which increases the electric field & electric flux linked with any imaginary loop considered parallel to the area of capacitor plates. This induces a displacement current in the direction of electric field, the magnetic field due to this current is calculated using the AML i.e.

If the capacitor plates has vacuum, then the conduction current will be zero, however due to displacement current the magnetic field at a point on the surface of loop L will be

If a loop is situated at r = R, then

If a loop is situated at r > R, then the loop encloses a displacement current equal to conduction current & the magnetic field becomes .

Also a compass needle place any where around a connecting wires or in the capacitor spacing deflects till the capacitor is undergoing charging or discharging.