Question

The capacitance of a spherical condenser is 1 microfarad if the spacing between the two sphere is 1 mm then radius of outer sphere

Answer 1

using formula,

C = $\frac{4\pi\epsilon_0ab}{a-b}$

where a is inner radius and b is outer radius of spherical shell in mm.

given, space between two spheres is 1mm

i.e., a - b = 1mm .....(1)

or, (a - 1) = b .....(2)

putting equations (1) And (2) in above expression.

C = $\frac{4\pi\epsilon_0a(a-1)}{1}$

C = 1 microfarad = 10^-6 F , $4\pi\epsilon_0=\frac{1}{k}=\frac{1}{9}\times10^{-9}$

so, 10^-6 = a(a - 1) × 10^-9 /9

or, 9 × 10³mm² = a(a - 1)

after solving we get, a = 95.37 mm

hence, radius of outer sphere is 95.37mm

Answer 2

Explanation:

hope this will help you