(a) Show that for a parallel-plate capacitor the displacement current is given by I_d = C dV/dt, where C is the capacitance and V the voltage across the capacitor.

(b) A parallel plate capacitor C = 5 nF is connected to an emf ← = ←₀ cos ωt, where ←₀ = 3 V and ω = 500π. Find the displacement current between the plates as a function of time. Neglect any resistance in the circuit.