A metal sphere of radius 1 ~m is charged with 10⁻² C in air. Its bulk modulus is 10¹¹ / 4 ² . The volume strain in the sphere is ( ₀= . pemittivity of free space)

Step-by-step solution

surface charge density = q 4 r² = 10⁻² 4 1 = 10⁻² 4 C / m ² strain = F A = 1 2 ² ₂ = 1 2 ₀ ( 10⁻² 4 )²= 10⁻⁴ 32 ² ₀ strain = stress k = 1 2 ² ₀ k where k= 10¹¹ 4 ² substituting and calculating we get strain = 10⁻¹⁵ 8 ₀