Question

A charge Q is placed at the center of an uncharged, hollow, conducting spherical shell. What is the electric field at a point outside the shell at a distance r from the center, and what is the net charge on the outer surface of the shell?

• A. E = 0, Net charge = 0
• B. E = (1/4\(\pi\epsilon_0\))(Q/r\(^2\)), Net charge = +Q
• C. E = (1/4\(\pi\epsilon_0\))(Q/r\(^2\)), Net charge = 0
• D. E = 0, Net charge = +Q

Hint:

Remember the key properties of conductors in electrostatic equilibrium:
- Electric field inside a conductor is zero.
- Any net charge on a conductor resides entirely on its outer surface.
- Induced charges distribute to cancel internal fields or maintain overall charge neutrality.

Answer 1

The Correct Option is B

A conductor always arranges its charges so the field inside its own material is zero. With \( +Q \) at the centre, the inner surface of the shell must pick up \( -Q \) to cancel that field within the metal, and since the shell overall was neutral, the outer surface is left with \( +Q \).

1. E = 0, net charge = 0: Cannot be right, since a nonzero charge sitting on a sphere always creates a field outside it.
2. E = kQ/r\(^2\), net charge = +Q: Matches the reasoning above exactly, the outer \( +Q \) acts like a point charge for anything outside the shell.
3. E = kQ/r\(^2\), net charge = 0: A zero net outer charge cannot itself produce this nonzero field.
4. E = 0, net charge = +Q: A nonzero outer charge cannot produce a zero field outside.

Therefore, the correct answer is E = (1/4\(\pi\epsilon_0\))(Q/r\(^2\)), Net charge = +Q.