A 0220A current is charging a capacitor that has circular pl

A 0.220-A current is charging a capacitor that has circular plates 15.6 cm in radius. The plate separation is 4.00 mm. (a) What is the time rate of increase of electric field between the plates? 3.25E11 V/m middot s (b) What is the magnetic field between the plates 5.00 cm from the center? .000002765 What is the electric flux through a circle of radius 5.00 cm lying parallel to the plates, midway between them ? T

Solution

(A) C = Q/V and C = e0 A / d

V = Q/C

dV/dt = (1/C) (dQ/dt) = I/c

and E = V/d

dE/dt = (dV/dt)/d = I / Cd

C = e0 A / d = (8.854 x 10^-12 x pi (0.156^2)) / (4 x 10^-3)

C = 1.69 x 10^-10 F

dE/dt = 0.22/ (1.69 x 10^-10 x 4 x 10^-3) = 3.25 x 10^11 V/m/s

(B) Integral of B.dL = e0 u0 d(flux)/dt

B (2 pi r) = e0 u0 pi r^2 dE/dt

B (2 x pi x 0.05) = (8.854 x 10^-11 x 4pi x 10^-7)(pi x 0.05^2) (3.25 x 10^11)

B = 9.04 x 10^-7 T