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.
$\left(ii\right)$ The electric potential at $O$ is.

​​​​​​​$[$1 Mark$]$

• A. $\frac{\sqrt{2}q}{\pi {\epsilon }_{0}a}$
• B. $\frac{\sqrt{3}q}{\pi {\epsilon }_{0}a}$
• C. $\frac{q}{\pi {\epsilon }_{0}a}$
• D. zero

Answer 1

The correct option is D zero

The electric potential at $O$ due to charges at $A,B,C\text{and}D$ is scalar sum potential due to each charge.
$V=V_A+V_B+V_C+V_D$

Here, $V_A=V_B=\frac{q}{4\pi {\epsilon }_0\left(\frac{a}{\sqrt{2}}\right)}$

$V_C=V_D=\frac{(-q)}{4\pi {\epsilon }_0\left(\frac{a}{\sqrt{2}}\right)}$

$V=2\left(\frac{q}{4\pi {\epsilon }_0\left(\frac{a}{\sqrt{2}}\right)}\right)+2\left(\frac{(-q)}{4\pi {\epsilon }_0\left(\frac{a}{\sqrt{2}}\right)}\right)$
$\therefore V=0$
So, option $\left(d\right)$ is correct.