Question

A uniformly charged thin spherical shell of radius R carries uniform surface charge density ofs per unit area. It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportional to(a) $\frac{1}{\epsilon_{0}}\sigma^{2}R^{2}$(b) $\frac{1}{\epsilon_{0}}\sigma^{2}R$(c) $\frac{1}{\epsilon_{0}}\frac{\sigma^{2}}{R}$(d) $\frac{1}{\epsilon_{0}}\frac{\sigma^{2}}{R^{2}}$

Answer 1

Correct option will be A

Solution :

 dA = 2 π R sin θ × Rdθ

      dF = σ^2 / 2ε_o × dA

     Component of dF along vertical axis = dF cos θ

     Total force = π /2 - 0  ∫ σ^2 / 2ε _o π R^2 sin 2θ dθ = σ^2 / 2ε0 × π R2

If F is proportional then the correct option would be A