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The electric field inside a uniformly charged spherical shell of radius R is:

  • A.directly proportional to the charge within the shell
  • B.inversely proportional to \(R^{2}\)
  • C.same as that outside the shell
  • D.zero
  • E.maximum at the centre

Answer: D

The field inside is zero.

By Gauss's law, a spherical surface drawn inside the shell encloses no charge, so the flux through it is zero. By symmetry the field is the same in magnitude everywhere on that surface and radial, so it must be zero at every point inside.

There is no charge within the shell for the field to be proportional to, the \(\frac{1}{R^{2}}\) and 'same as outside' options describe the field outside, and nothing makes it maximum at the centre.

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