A parallel plate capacitor with circular plates of radius R=10 ~cm has a capacitance of 50 ~pF . It is being charged such that the potential difference between the plates is changing at a constant rate of 4 10^9 ~V/s . The displacement current passing through a concentric circular sub-region of radius r=5 ~cm between the plates is ________ mA .

Step-by-step solution

The total displacement current i_d is given by: i_d = C dV dt i_d = (50 10⁻¹² ~F ) (4 10^9 ~V/s ) = 200 10⁻³ ~A = 200 ~mA The displacement current is uniformly distributed over the area of the circular plates. The area of the plates is A = R^2 and the area of the sub-region is A₀ = r^2 . The displacement current i_ d, A₀ through the sub-region is: i_ d, A₀ = i_d ( A₀ A ) = i_d ( r R )^2 i_ d, A₀ = 200 ~mA ( 5 10 )^2 = 200 1 4 = 50 ~mA Answer: 50