Question

Suppose that a parallel-plate capacitor has circular plates with radius R = 75.0 mm and a plate separation of 5.2 mm. Suppose also that a sinusoidal potential difference with a maximum value of 140 V and a frequency of 60 Hz is applied across the plates; that is V=(140.0 V)sin((2.*π)*(60 Hz * t)).

a) Find Bmax(R), the maximum value of the induced magnetic field that occurs at r = R.

b) Find B(r = 37.5 mm).

c) Find B(r = 150.0 mm).

d) Find B(r = 225.0 mm).

Answer 1

a)

w = 2pi*f

w = 2pi*60

w = 120 c/s

Bmax = ooRVmaxw / 2d

Bmax = (4pi x 10^-7 x 8.85 x 10^-12 x 75 x 10^-3 x 140 x 120pi) / (2 x 5.2 x 10^-3)

Bmax = 4.23 x 10^-12 T

b)

Bmax = ooRVmaxw / 2d

Bmax = (4pi x 10^-7 x 8.85 x 10^-12 x 37.5 x 10^-3 x 140 x 120pi) / (2 x 5.2 x 10^-3)

Bmax = 2.12 x 10^-12 T

c)

Bmax = ooRVmaxw / 2d

Bmax = (4pi x 10^-7 x 8.85 x 10^-12 x 150 x 10^-3 x 140 x 120pi) / (2 x 5.2 x 10^-3)

Bmax = 8.47 x 10^-12 T

d)

Bmax = ooRVmaxw / 2d

Bmax = (4pi x 10^-7 x 8.85 x 10^-12 x 225 x 10^-3 x 140 x 120pi) / (2 x 5.2 x 10^-3)

Bmax = 1.27 x 10^-11 T