Question

A spherical capacitor is formed from two concentric, spherical, conducting shells separated by vacuum. The inner sphere has radius 16 cm and the capacitance is 113 pF. What is the radius of the outer sphere? (Give your answer in decimal using cm as unit)

Answer 1

19 cm

Step-by-step explanation:

inner radius, a = 16 cm, C = 113 p F = 113 x 10^-12 F

Let b cm be the radius of outer sphere.

The formula of capacitance of spherical capacitor is given by

C = 4π∈0 a b / (b - a)

a b / ( b - a) = C / 4π∈0

a b / ( b - a ) = 113 x 10^-12 x 9 x 10^9

a b / ( b - a ) = 1.017

16 x 10^-2 x b x 10^-2 = 1.017( b - 16) x 10^-2

0.16 b = 1.017 b - 16.272

0.857 b = 16.272

b = 19 cm