Question

Write Maxwell's generalization of Ampere's Circuital Law. Show that in the process of charging a capacitor, the current produced within the plates of the capacitor is 

Where ϕ_E  is the electric flux produced during charging of the capacitor plates.

Answer 1

Ampere's circuital law is given by as 

But for a circuit containing capacitor, during its charging / discharging the current within the plates of the capacitor varies, (producing displacement current i_d).

Therefore,the above equation,as generalized by Maxwell,is given as 

During the Process of charging of capacitor, electric flux (ϕ_E) between the plates of capacitor changes with time,

which produces the current within the plates of capacitor. This current being proportional to dϕ∈/dt, we have