Question

A metal sphere of radius 1 m is charged with 10^-2 C in air. Its bulk modulus is `10^11/(4pi^2) "N"/"m"^2`. The volume strain in the sphere is (ε₀ = permittivity of free space.)

Options

• `10^(-15)/(6epsilon_0)`

• `10^(-15)/(16epsilon_0)`

• `10^(-15)/(8epsilon_0)`

• `10^(-15)/(2epsilon_0)`

Answer 1

`10^(-15)/(8epsilon_0)`

Explanation:

`sigma = "q"/(4pi"r"^2) = (10^-2)/(4pi)`

Force per unit area (stress) = `sigma^2/(2epsilon_0)`

`= 10^-4/(16 pi^2) xx 1/(2epsilon_0)`

`= 10^-4/(32 pi^2epsilon_0)`

Strain = `"Stress"/"k" = 10^-4/(32 pi^2epsilon_0) xx (4pi^2)/10^11 = (10^-15)/(8epsilon_0)`