$A$ test charge $q$ is moved in the electric field of a point charge $Q$ along two different closed paths as shown in the figure. The first path has sections along and perpendicular to the lines of the electric field. The second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases?

(N/A) The electrostatic field created by a point charge $Q$ is a conservative field.
In a conservative field,the work done by the electric force on a charge moving along any closed path is always zero.
This is because the work done in a conservative field depends only on the initial and final positions of the charge,not on the path taken.
Since both paths are closed loops,the displacement of the test charge $q$ starts and ends at the same point in both cases.
Therefore,the work done by the electric force in both cases is zero,and they are equal to each other.