Question

Two equipotential surfaces A and B are separated by a distance x. The work done in moving a charge -q from A to B is (Assume $\varepsilon_0$ = permittivity of free space)

• A. $\dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{q}{r}$
• B. $\dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{-q}{r}$
• C. $\dfrac{1}{4\pi\varepsilon_0} \cdot \dfrac{q}{r^2}$
• D. zero

Hint:

No work is done in moving a charge along or between equipotential surfaces.

Answer 1

The Correct Option is D

By definition, the potential difference between two points on an equipotential surface is zero.
Since $W = q \cdot \Delta V$, and $\Delta V = 0$ between points A and B on equipotential surfaces,
$\Rightarrow W = -q \cdot 0 = 0$