Question

Two small spheres each carrying a charge $q$ are placed $r$ metre apart. If one of the spheres is taken around the other one in a circular path, the work done will be equal to:
A. \[{\text{force between them}} \times r\]
B. \[{\text{force between them}} \times 2\pi r\]
C. \[\dfrac{{{\text{force between them}}}}{{r\pi r}}\]
D. ${\text{zero}}$

Answer 1

Hint: To solve this type of question, one must know about work done, potential energy of charges and equipotential surfaces. Here we have used concepts of these terms to get the required solution and Equipotential or isopotential in mathematics and physics refers to a region in space where every point in it is at the same potential.

Complete step by step answer:
We know that if \[W\] is the work done in bringing a unit positive charge $q$ from infinity to a point in the field, the electric potential $V$ at this point is given by:
$V = \dfrac{W}{q} \\
\Rightarrow W = qV \\ $
And we know that electric potential is $V = \dfrac{{kQ}}{r}$
Combining both the equation,
\[W = \dfrac{{kqQ}}{r}\]
Which is nothing but electric potential energy. So, we can say that electric potential energy is related to work done. So, we can say if potential energy will be zero then work done also will be zero.

Therefore, the correct option is D.

Note: In other words, note that, Electric field is conservative. So, work done in taking a charge on the closed path is zero or two small spheres, each carrying a charge $q$ are placed at a distance of $r$ metre apart and they interact with force$F$ . If one of the spheres is taken around the other once in a circular path, the work done will be equal to.Work done in equipotential surface is zero.