question_answer

A charge q is fixed. Another charge Q is brought near it and rotated in a circle of radius r around it. Work done during rotation is

A)  zero                     

B)        \[\frac{Qq}{4\pi G{{\varepsilon }_{0}}r}\]

C) \[\frac{Qq}{2\pi G{{\varepsilon }_{0}}r}\]            

D)         None of these

Correct Answer: A

Solution :

Potential due to charge\[(q)\]at point\[(r)\]is given by                 \[V=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{q}{r}\] Since, charge\[Q\]is rotated in a circle of radius\[r\], hence its potential remains same at all points on the path, hence\[\Delta V=0\]. Also, work done\[=q\Delta V\] where\[q\]is charge and\[\Delta V=0\]. \[\therefore \]Work done = 0.