Question

Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2L$ (see figure). The electric potential at point A, midway between the two charges $+q$ and $+q$, is :
[NEET- 2011 (Pre)]

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

Answer 1

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

Potential at point $A$,

$V_A=\frac{kq}{L}+\frac{kq}{L}-\frac{kq}{\sqrt{L^2+(2L{)}^2}}-\frac{kq}{\sqrt{L^2+(2L{)}^2}}$

$\Rightarrow V_A=\frac{kq}{L}\times 2-2\frac{kq}{L\sqrt{5}}$

As, $k=\frac{1}{4\pi {\epsilon }_0}$

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

Hence, $\left(C\right)$ is the correct answer.