Question

Four charges $2q,q,–q$ and $–q$ are placed at corners of a square of side length $a.$ The electrostatic potential at the centre of the square will be equal to

$[$0.77 Mark$]$

• A. $\frac{\sqrt{2}q}{8\pi {\epsilon }_{0}a}$
• B. $\frac{\sqrt{2}q}{4\pi {\epsilon }_{0}a}$
• C. $\frac{3\sqrt{2}q}{4\pi {\epsilon }_{0}a}$
• D. $\frac{\sqrt{2}q}{\pi {\epsilon }_{0}a}$

Answer 1

The correct option is B $\frac{\sqrt{2}q}{4\pi {\epsilon }_{0}a}$


The net electric potential at a point due to a system of charged particles is the scalar sum of electric potential due to individual charged particles at that point.
$V=\frac{k\left(2q\right)}{\left(\frac{a}{\sqrt{2}}\right)}+\frac{kq}{\left(\frac{a}{\sqrt{2}}\right)}+\frac{k(-q)}{\left(\frac{a}{\sqrt{2}}\right)}+\frac{k(-q)}{\left(\frac{a}{\sqrt{2}}\right)}(\text{where}k=\frac{1}{4\pi {\epsilon }_0})$
$=\frac{\sqrt{2}kq}{a}=\frac{\sqrt{2}}{4\pi {\epsilon }_0}\frac{q}{a}$