Question: A shell of radius R has a charge Q spread uniformly on its surface. The potential at distance of 3R ...

Question

A shell of radius R has a charge Q spread uniformly on its surface. The potential at distance of 3R from center is

Answer 1

Solution

The electric potential at a distance $r$ from the center of a uniformly charged spherical shell of radius $R$ and total charge $Q$ is given by:

V(r) = \begin{cases} \frac{kQ}{r} & \text{for } r > R \\ \frac{kQ}{R} & \text{for } r \le R \end{cases}

In this problem, the point where the potential is required is at a distance $r = 3R$ from the center. Since $3R > R$ , the point is outside the spherical shell.

Therefore, we use the formula for $r > R$ :

V(3R) = \frac{kQ}{3R}