Question

FIGURE P25.71 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center.

Short answer

The electric potential as the center is$\frac{kQ}{R}$.

Step-by-step solution

Given Information

We need to find an expression for the electric potential at the center.

Explanation

Let us consider that if we have more than one point, the potential can be written as

$V=k\sum \frac{q}{r}$.

In this case, one might first thing we need to integrate, but in fact we can't, as all the charge parts, however we split them, are equally distant from the point of interest. That is, we have

$$\begin{gathered} V=\frac{k}{R}\sum q \\ V=\frac{kQ}{R} \end{gathered}$$