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

Options

  1. A1 ε 0 σ 2 R 2
  2. B1 ε 0 σ 2 R
  3. C1 ε 0 σ 2 R
  4. D1 ε 0 σ 2 R 2

Correct answer

A. 1 ε 0 σ 2 R 2

Step-by-step solution

The electrostatic pressure at a point on the charged conducting surface of surface charge density σ is d F d A = σ 2 2 ε 0 Due to the electrostatic repulsion between the charged hemisphere, there is a requirement of an external force F on each hemisphere which will balance the electrostatic force due to the other hemisphere. For the given case, consider a thin ring at an angle θ away from the diametrical axis. Now lets take a small ring of angle d θ around this ring, as shown in the figure

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