A solid non-conducting sphere of radius R has a total charge Q distributed uniformly throughout its volume. The magnitude of the potential difference between the centre of the sphere and a point on its surface is:

Step-by-step solution

For a uniformly charged solid non-conducting sphere, the electric potential at a distance r from the centre (where r R ) is given by: V(r) = 1 4 ₀ Q(3R^2 - r^2) 2R^3 At the centre of the sphere ( r = 0 ), the potential is: V_ centre = 1 4 ₀ 3Q 2R At the surface of the sphere ( r = R ), the potential is: V_ surface = 1 4 ₀ Q(3R^2 - R^2) 2R^3 = 1 4 ₀ Q R The magnitude of the potential difference between the centre and the surface is: V = V_ centre - V_ surface V = 1 4 ₀ ( 3Q 2R - Q R ) V = 1 4 ₀ Q 2R Answer: 1 4 ₀ Q