• summary_type: application
• word_count: 150

For a parallel plate capacitor being charged: I_d = epsilon_0 * d(Phi_E)/dt = epsilon_0 * A * dE/dt. Since E = Q/(epsilon_0A) between the plates: I_d = dQ/dt = I_c. The displacement current density j_d = epsilon_0 * dE/dt (A/m^2). Between the plates, the magnetic field at radius r from the axis: B = mu_0I_dr/(2piR^2) for r < R (inside the plates), and B = mu_0I_d/(2pir) for r > R (same as a wire carrying I_c). Here R is the plate radius. If the capacitor voltage is V(t) = V_0sin(omegat): E = V/d, dE/dt = V_0omegacos(omegat)/d, and I_d = epsilon_0AV_0omegacos(omegat)/d = CV_0omegacos(omegat) (since C = epsilon_0*A/d). JEE may ask for I_d given dV/dt or dE/dt.