Question

In the electric field of a fixed point charge $q$, a certain charge is carried from point $A$ to $B,C,D$ and $E$ as shown in the figure. Then the work done :

• A. Is least along the path $AB$
• B. Is least along the path $AD$
• C. Is zero along all the paths
• D. Is least along the path $AE$

Answer 1

The correct option is C Is zero along all the paths

Points $A,B,C,D$ and $E$ all lies on the circumference of a circle, with charge $q$ at its center.
Therefore, we can say that potential energy of an external charge (Say $Q$), will be same at all of these points.

We know that :

$\text{Work done = Change in electrostatic potential energy}$

Or, $W=\Delta P.E.$

Since, $P.E.$ of external charge is same at every given point, no work will be done in moving the external charge $\left(Q\right)$ along any of the given paths.

Hence, option $\left(c\right)$ is the correct answer.