Question

A spherical capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has a radius of ra = 12.4 cm , and the outer sphere has a radius of rb = 14.9 cm . A voltage of 120 V is applied to the capacitor.

a)

What is the capacitance of the capacitor?

Use ϵ0 = 8.85×10⁻¹² F/m for the permittivity of free space

b) What is the magnitude E1 of the electric field E⃗  at radius r= 12.8 cm , just outside the inner sphere?

c) What is the magnitude of E⃗  at r= 14.7 cm , just inside the outer sphere?

Answer 1

A)

Capacitance, C = 4 pi e0/(1/a - 1/b)

C = (4 pi x 8.85 x 10^-12)/(1/0.124 - 1/0.149) = 8.22 x 10^-11 F

B)

Charge, Q = CV

Q = 8.22 x 10^-11 x 120 = 9.86 x 10^-9 C

E1 = (9.86 x 10^-9)/(4 pi x 8.85 x 10^-12 x 0.128^2) = 5411.33 N/C

C)

E1 = (9.86 x 10^-9)/(4 pi x 8.85 x 10^-12 x 0.147^2) = 4102.88 N/C

Comment in case any doubt please rate my answer...