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GATE 2017 EE (EE2) – Question 12

Electromagnetic Fields · Coulomb's Law, Electric Field Intensity, Electric Flux Density, Gauss's Law, Divergence · 1 mark · Multiple choice

A solid sphere of radius 5 cm is made of a perfect electric conductor. If one million electrons are added, they are distributed

  1. uniformly throughout the entire volume
  2. uniformly over the outer surface
  3. concentrated around the centre
  4. along a straight line through the centre

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Correct answer: (B) uniformly over the outer surface

Explanation

At electrostatic equilibrium the field inside a conductor is zero. Any excess free charge moves to its outer surface rather than remaining in the conducting bulk.

The sphere is geometrically symmetric and no external asymmetric field is specified, so the surface charge density is uniform. The added electrons therefore spread **uniformly over the outer surface, B**. The amount of charge changes the potential, not this symmetry argument.

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