Question

In the given figure change $+ \,Q$ is placed at the center of a dotted circle. Work done in taking another charge $+ q$from A to B is ${W_1}$ and from B to C is ${W_2}$. Which one of the following is correct ${W_1} > {W_2},{W_1} < {W_2}?$

Answer 1

students should recall the concept of equipotential surface that if the points of a circle are at the same distance from the center of the dotted circle, then the potential distance at these points is the same but not work done. Use the concept and reach the solution.
Given: A dotted circle is given having charge $+ Q$ is placed at the center of a dotted circle. Work done in taking another charge $+ q$ from A to B is ${W_1}$and from B to C is ${W_2}$.

Complete step by step answer:
In the figure of the dotted circle, A, B and C are at the same distance from the center of the circle. So, it is clear that the potential at all these three points will be same but not work done ${W_1},{W_2}$ The${W_1}\,and\,{W_2}$ should be zero because the potential difference is zero.
As $VA\, - \,VB\, = \,VB\, - VC$ magnitude of work done is the same.
So,${W_1}\, = \,{W_2}$ because
$W = \,VQ$ here $V$ and $Q$ are the same.

Note: It is noted that if all the points are at same distance from the center of the dotted circle, then the potential at all these points will be the same but not work done. Here, ${W_1}\, = \,{W_2}$ b because $W = VQ$ here V and Q are the same.