Question

A point charge $q$ is rotated along a circle in the electric field generated by another point charge $Q$. The work done by electric field on the rotating charge in one complete revolution is

• A. Zero
• B. Positive
• C. Negative
• D. Zero, if the charge $Q$ is at centre and nonzero otherwise

Answer 1

The correct option is A Zero

When the rotating charge $q$ completes one revolution it will attain its initial position. So

$\therefore V_f=V_i=V$

Where, $V=$ electric potential


The work done by electric field due to charge $Q$ on charge $q$ in one complete revolution is given by

$\frac{W_{ext(i\to f)}}{q}=V_f-V_i$

$\Rightarrow \frac{-W_{elec(i\to f)}}{q}=V_f-V_i=\Delta V$

$\Rightarrow \frac{-W_{elec}}{q}=0$

$\therefore W_{elec}=0$

So, option $\left(a\right)$ is correct.

$\begin{array}{c}\text{Why this question?}\\ \text{Tip: If q would have been rotating around}\\ \text{centre as charge Q, then for any}\\ \text{moment on circle}{V}_i=V_f=\frac{KQ}{r}.\text{Thus,}{W}_{elec}=0.\\ \text{Caution: In one complete revolution}\\ \text{work done by electric forces will always}\\ \text{be zero, despite any position of the charge}Q\\ \end{array}$