Question

A shell of radius R has a charge Q spread uniformly on its surface. The potential at the surface of the shell is

• A. kQ/R
• B. 0
• C. 2KQ/R
• D. 3kQ/2R

Answer 1

Answer: (A)

kQ/R

Answer 2

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:

For $r > R$: $V(r) = \frac{1}{4\pi\epsilon_0} \frac{Q}{r}$

For $r \le R$: $V(r) = \frac{1}{4\pi\epsilon_0} \frac{Q}{R}$

We are asked to find the potential at the surface of the shell, which corresponds to $r = R$.

Using the formula for $r \le R$ and setting $r = R$, we get:

$V(R) = \frac{1}{4\pi\epsilon_0} \frac{Q}{R}$

Using the formula for $r > R$ and taking the limit as $r \to R^+$, we get:

$V(R) = \lim_{r \to R^+} \frac{1}{4\pi\epsilon_0} \frac{Q}{r} = \frac{1}{4\pi\epsilon_0} \frac{Q}{R}$

Both formulas give the same result at the surface.

Let $k = \frac{1}{4\pi\epsilon_0}$. Then the potential at the surface of the shell is $V(R) = k \frac{Q}{R}$.