# Potential difference between centre and surface of the sphere of radius R and uniform volume charge density ρ within it will be

Q. Potential difference between centre and surface of the sphere of radius R and uniform volume charge density ρ within it will be

(a) $\displaystyle \frac{\rho R^2}{6\epsilon_0}$

(b) $\displaystyle \frac{\rho R^2}{4\epsilon_0}$

(c) $\displaystyle \frac{\rho R^2}{3\epsilon_0}$

(d) $\displaystyle \frac{\rho R^2}{2\epsilon_0}$

Ans: (a)
Sol: Charge on Sphere is

$\displaystyle q = \frac{4}{3}\pi R^3 \rho$

Electric Potential at the centre

$\displaystyle V_o = \frac{1}{4\pi \epsilon_0}\frac{3q}{2R}$

Electric Potential at the Surface

$\displaystyle V_P = \frac{1}{4\pi \epsilon_0}\frac{q}{R}$

Potential difference between centre and surface

$\displaystyle = \frac{1}{4\pi \epsilon_0}\frac{3q}{2R} – \frac{1}{4\pi \epsilon_0}\frac{q}{R}$

$\displaystyle = \frac{1}{4\pi \epsilon_0}\frac{q}{2R}$

$\displaystyle = \frac{1}{4\pi \epsilon_0 (2R)}(\frac{4}{3}\pi R^3 \rho)$

$\displaystyle = \frac{\rho R^2}{6\epsilon_0}$