Question

A metal sphere of radius 1 m is charged with 10^-2 C in air. Its bulk modulus is 10¹¹/4π². The volume strain in the sphere is ______ 

(ε₀ = permittivity of free space)

पर्याय

• `10^-14/(8epsilon_0)`

• `10^-12/(4epsilon_0)`

• `10^-15/(8epsilon_0)`

• `10^-1/(6epsilon_0)`

Answer 1

A metal sphere of radius 1 m is charged with 10^-2 C in air. Its bulk modulus is 10¹¹/4π². The volume strain in the sphere is `underline(10^-15/(8epsilon_0))`.

Explanation:

surface charge density `sigma = q/(4pir^2) = (10^-2)/(4pi xx 1) = (10^-2)/(4pi)` C/m²

strain = `F/A = 1/2 sigma^2/epsilon_2 = 1/(2epsilon_0) xx (10^-2/(4pi))^2 = (10^-4)/(32pi^2 epsilon_0)`

strain = `"stress"/k = 1/2 sigma^2/(epsilon_0k)`

where k = `10^11/(4pi^2)`

substituting and calculating we get strain = `10^-15/(8epsilon_0)`