Question:

A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre?

Increases as r increases for rR

Zero as r increases for r<R, increases as r increases for r>R

Zero as r increases for r<R, decreases as r increases for r>R

Decreases as r increases for rR

Solution:

Correct option is B. Zero as r increases for r<R, decreases as r increases for r>R
Charge Q will be distributed over the surface of hollow metal sphere
(i) For r < R (inside)
By Gauss law, ∮Ein⋅dS = qen/ε0 = 0 ⇒ Ein = 0 (∵ qen = 0)
(ii) For r > R (out side)
∮E₀⋅dS = qen/ε0
Here, qen = Q (∵ qen = Q)
∴ E₀4πr² = Q/ε0
∴ E₀ ∝ 1/r²