A uniformly charged thin spherical shell of radius $R$ carries a uniform surface charge density of $σ$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to

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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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