The planar circular plates of a capacitor are being charged. At a given moment t

Question

The planar circular plates of a capacitor are being charged. At a given moment the charge is being built up at the rate The plates have a radius R and a separation d. Show that the magnetic held due to the displacement current midway between the plates at a radius equal to half the plate radius is given by: mu_0/4 pi 1/R dq/dt Given that the radius of the plate is R = 0.1 m. and the plate separation d = 1cm. Calculate the magnetic field due to the displacement current midway between the plates at a radius equal to half the plate radius, if the charge builds up at a rate of 1 C/s..

Explanation / Answer

Midway between the plates, let the magnetic field be B at distace R/2 from the centre of the plates
consider an amperical loop
from ampere's law

B*2pi(R/2) = mu*I(en)
B = mu*I(en)/pi*R
Now, I(en) = I(total)*pi*(R/2)^2/pi*R^2 = I(total)/4 = dq/4dt
so B = mu*dq/4*pi*R*dt .. (1)

R = 0.1m
dQ/dt = 1 C/s

B = 10^-7*1/0.1 = 10^-6 T

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