Question

Two metal spheres having charge densities 5μC/m² and -2μC/m² with radii 2mm and  1mm respectively are kept in a hypothetical closed surface. Calculate total normal electric induction over the closed surface.

Answer 1

σ₁ = 5 μC/m²

σ₂ = -2 μC/m²

r₁ = 2 mm

r₂ = 1 mm

q₁ = σ₁4π r₁²

q₂ = σ₂4π r₂²

T.N.E.I. = q₁ + q₂

∴T.N.E.I. = 4π(σ₁r₁² + σ₂r₂²)

∴T.N.E.I. = 4π(5 × 10^-6 × 4 × 10^-6 + (−2) × 10^-6 × 1 × 10^-6)

∴T.N.E.I. = 72π × 10^-12 C

∴T.N.E.I. = 226.08 × 10^-12 C

Hence, the total normal electric induction over the closed surface is 226.08 × 10^-12 C.