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JEE Advanced2010PhysicsElectrostaticsActual

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

Options

  1. A1 ₀ ^2 R^2
  2. B1 ₀ ^2 R
  3. C1 ₀ ^2 R
  4. D1 ₀ ^2 R^2

Correct answer

A. 1 ₀ ^2 R^2

Step-by-step solution

Electrical force per unit area = 1 2 ₀ E^2 = 1 2 ₀ ( ₀ )^2= ^2 2 ₀ Projected area = R^2 net electrical force = ( ^2 2 ₀ ) ( R^2 ) In equilibrium, this force should be equal to the applied force. F= ^2 R^2 2 ₀ or F ^2 R^2 ₀ The correct option is (a).

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