Question

Four charges $+q,+q,-q\text{and}-q$ are placed respectively at the corners $A,B,C\text{and}D$ of a square of side $a$ arranged in the given order. $E\text{and}F$ are midpoints of side $BC$ and $CD$ respectively. $O$ is the center of the square.

$\left(iii\right)$ The work done in carrying a charge $e$ from $O$ to $E$ is

​​​​​​​$[$1 Mark$]$

• A. $\frac{\sqrt{2}qe}{\pi {\epsilon }_{0}a}$
• B. zero
• C. $\frac{\sqrt{2}qe}{\pi {\epsilon }_{0}a}[\frac{1}{\sqrt{5}}-1]$
• D. $\frac{\sqrt{2}qe}{\pi {\epsilon }_{0}a}[\frac{1}{\sqrt{5}}+1]$

Answer 1

The correct option is B zero

Work done in carrying a charge $e$ from $O$ to $E$
$W=e(V_E-V_O)$
The charge at $A\text{and}D$ are opposite and equidistant from $O$ and $E$. So potential due to charges at $A\text{and}D$ at points $O$ and $E$ will cancel each other.
Likewise, the charge at $B\text{and}C$ are opposite and equidistant from $O$ and $E$. So potential due to charges at $B\text{and}C$ at points $O$ and $E$ will cancel each other.
Net Electric potential at $O$ as well as at $E$ is zero i.e $V_O=0$ and $V_E=0$
$\therefore W=0$
So, option $\left(b\right)$ is correct.