Question

Four charges $–q,–q,+q$ and $+q$ are placed at the corners of a square of side $2L$ is shown in figure. The electric potential at point $A$ midway between the two charges $+q$ and $+q$ is

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{L}(1-\frac{1}{\sqrt{5}})$
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{q}{2L}(1-\frac{1}{\sqrt{5}})$
• C. Zero
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{L}(1+\frac{1}{\sqrt{5}})$

Answer 1

The correct option is A $\frac{1}{4\pi {\epsilon }_0}\frac{2q}{L}(1-\frac{1}{\sqrt{5}})$

Electric potential at point A = $V_A$ (say)

$V_A$ = Sum of electric potentials at point A due to each individual charge

$=\frac{kq}{L}+\frac{kq}{L}-\frac{kq}{\sqrt{5}L}-\frac{kq}{\sqrt{5}L}$

$=\frac{2kq}{L}(1-\frac{1}{\sqrt{5}})$

$=\frac{2q}{4\pi {\epsilon }_{0}L}(1-\frac{1}{\sqrt{5}})$