Q. A positive point charge $q$ is carried from a point $B$ to a point $A$ in the electric field of a point charge +$Q$ at $O$. If the permittivity of free space is $\varepsilon_{0}$, the work done in the process is given by (where a =OA and $b = OR$)
A) $\frac{qQ}{4\pi\varepsilon_{0}}\left( \frac{1}{a} + \frac{1}{b} \right)$
B) $\frac{qQ}{4\pi\varepsilon_{0}}\left( \frac{1}{a} - \frac{1}{b} \right)$
C) $\frac{qQ}{4\pi\varepsilon_{0}}\left( \frac{1}{a^{2}} - \frac{1}{b^{2}} \right)$
D) $\frac{qQ}{4\pi\varepsilon_{0}}\left( \frac{1}{a^{2}} + \frac{1}{b^{2}} \right)$
Explanation
(b) $W_{BA} = q\left( V_{A} - V_{B} \right) = q\left\lbrack \frac{Q}{4\pi\varepsilon_{0}a} - \frac{Q}{4\pi\varepsilon_{0}b} \right\rbrack$
$= \frac{qQ}{4\pi\varepsilon_{0}}\left\lbrack \frac{1}{a} - \frac{1}{b} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.