The electric field at 2R from the centre of a uniformly charged non-conducting sphere of radius R is E. The electric field at a distance R/2 from the centre will be

(a) Zero

(b) 2E

(c) 4E

(d) 16E

Let the total charge on the sphere be = Q.

The sphere is uniformly charged.

Let,

Charge density = ρ

... (1)

The electric field at a distance 2 R due to the sphere = E

... (2)

To Find: Electric field at a distance R/2 from the centre of sphere = E₁

First, we find the charge enclosed within the sphere of radius R/2.

Q1 = charge enclosed