Question

In the figure below, the capacitor with circular plates of radius R = 20.0 cm is connected to a source of emf ee= em sin at, where rm-240 V and ω 120 rad/s. The maximum value of the displacement current is id = 7.50 μA. Neglect fringing of the electric field at the edges of the plates sin ot (a) What is the maximum value of the current i in the circuit? (b) what is the maximum value of ddedt, where ФЕ is the electric flux through the region between the plates? V m/s (c) What is the separation d between the plates? (d) Find the maximum value of the magnitude of B between the plates at a distance r 13.0 cm from the center.

Answer 1

We have the maximum value of current in the given circuit is equal to the displacement current i_d in the gap of the plates therefore i_max = 7.5 mu A WE have displacement current i_d = epsilon_0 d Q_E . dt d phi_epsilon/dt = i_d . epsilon_0 = (7.5 mu A)/(8.85 times 10^negative 12 F /m) = 0.84745 times 10^6 vm/s = 8.4745 times 10^5 vm/s Also we have displacement current i_d = c dv/dt but capacitance cc = epsilon_0 A . d A is area of the plates = pi R^2 R = 20 times 10^negative 2 m And dv/dt = d/dt (epsilon m sin infinity t) therefore d = epsilon_0 pi R^2 infinity Epsilon_n I_d max = 4268.3904 times 10^negative 6 = = 4 .268 times 10^negative 3 m