# Write Maxwell'S Generalization of Ampere'S Circuital Law - Physics

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 I=varepsilon_0 (dphi_E)/dt,where ΦE is the electric flux produced during charging of the capacitor plates.

#### Solution

Maxwell's generalisation of Ampere's circuital law is given as follows:

ointvecB.vec"dl"=mu_0(I+I_D)=mu_0(I+varepsilon_0 (dphi)/dt)

Consider that a parallel capacitor C is charging in a circuit.

The magnitude of electric field between the two plates will be E=q/(varepsilon_0 A)and is perpendicular to the surface of the plate.

phi_E=vecE.vecA=EA cos0=q/(varepsilon_0 A)xxA=q/varepsilon_0

=>(dphi_E)/dt=(d(q/varepsilon_0))/dt

=>(dq)/dt=varepsilon_0(dphi_E)/dt ("Here, dq/dt is rate of change of charge with time.")

=>I=varepsilon_0(dphi_E)/dt

Concept: Ampere’s Circuital Law
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