Electrostatics 7 Question 8

8. A uniformly charged thin spherical shell of radius R carries 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

(2010)

(a) 1ε0σ2R2

(b) 1ε0σ2R

(c) 1ε0σ2R

(d) 1ε0σ2R2

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Solution:

  1. Electrical force per unit area =12ε0E2

=12ε0σ2ε0=σ22ε0

Projected area =πR2

Net electrical force =σ22ε0(πR2)

In equilibrium, this force should be equal to the applied force.

F=πσ2R22ε0 or Fσ2R2ε0

The correct option is (a).



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