Question

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 permitivity of free space is ${\epsilon }_0$, the work done in the process is given by

• A. $\frac{qQ}{4\pi {\epsilon }_o}\left(\frac{1}{a}+\frac{1}{b}\right)$
• B. $\frac{qQ}{4\pi {\epsilon }_o}\left(\frac{1}{a}-\frac{1}{b}\right)$
• C. $\frac{qQ}{4\pi {\epsilon }_0}\left(\frac{1}{a^2}-\frac{1}{b^2}\right)$
• D. $\frac{qQ}{4\pi {\epsilon }_o}\left(\frac{1}{a^2}+\frac{1}{b^2}\right)$

Answer 1

Answer: (B)

$W_{BA}=q\left(V_A-V_B\right)$
$=q\left[\frac{Q}{4\pi {\epsilon }_{0}a}-\frac{Q}{4\pi {\epsilon }_{0}b}\right]=\frac{qQ}{4\pi {\epsilon }_0}\left[\frac{1}{a}-\frac{1}{b}\right]$