A parallel plate capacitor of area A=50 ~cm ^2 is being charged. Consider a hypothetical plane surface of area A₀=5 ~cm ^2 inside the capacitor and parallel to the plates. At a certain instant, the displacement current passing through the surface A₀ is 200 ~mA . The rate at which charge is accumulating on the capacitor plates at this instant is ________ A .

Step-by-step solution

The displacement current density J_d is uniform between the plates of the capacitor. J_d = i_ d, A₀ A₀ = i_d A Total displacement current i_d = i_ d, A₀ ( A A₀ ) i_d = 200 ~mA ( 50 5 ) = 2000 ~mA = 2 ~A The rate of accumulation of charge on the plates is equal to the conduction current i_c , which is equal to the total displacement current i_d . dq dt = i_c = i_d = 2 ~A Answer: 2