Question

A solid sphere of radius R carries charge Q distributed uniformly throughout its volume. Find the potential difference from the sphere's surface to its center. Express your answer in terms of the variables R, Q and Coulomb constant k.

Answer 1

Answer:

$\Delta V = \frac{kQ}{2R}$

Explanation:

As we know that electric field inside the solid sphere is given by

$E = \frac{kQr}{R^3}$

here we know that

Q = total charge on the sphere

R = radius of the sphere

r = distance from the center of the sphere

now by the relation of potential difference and electric field we know that

$\Delta V = -\int E. dr$

now for the potential difference between centre and the surface we have

$\Delta V = -\int_R^0 \frac{kQr}{R^3} dr$

$\Delta V = \frac{kQ}{2R}$