A thin spherical shell of radius R is cut into two equal halves and then each of its halves is charged to the same uniform surface charge density σ . If F is the force exerted on each half to keep them at equilibrium, then F is proportional to

Question

A thin spherical shell of radius R is cut into two equal halves and then each of its halves is charged to the same uniform surface charge density σ . If F is the force exerted on each half to keep them at equilibrium, then F is proportional to, 1 ε 0 σ 2 R, 1 ε 0 σ 2 R, 1 ε 0 σ 2 R 2, 1 ε 0 σ 2 R 2

MARKS App · Accepted Answer

Electrical force per unit area = 1 2 ε 0 E 2 = 1 2 ε 0 σ ε 0 2 = σ 2 2 ε 0 Projected area = π R 2 ∴ Net electrical force = σ 2 2 ε 0 π R 2 In equilibrium, this force should be equal to the applied force. ∴ F = π σ 2 R 2 2 ε 0 or F ∝ σ 2 R 2 ε 0

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