Question

Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2\text{L}$. The electric potential at point $\text{A}$, midway between the two charges $+q$ and $+q$, is:-

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

Answer 1

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


Since, electric potential is a scalar quantity, so we can add directly for net potential at point $\text{A}$

$\therefore V_{net}=V_{\text{due to B}}+V_{\text{due to C}}+V_{\text{due to D}}+V_{\text{due to E}}$

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

$\Rightarrow V_{net}=\frac{2kq}{L}-\frac{2kq}{\sqrt{5}L}$

$\Rightarrow V_{net}=\frac{1}{4\pi {ϵ}_0}\frac{2q}{L}(1-\frac{1}{\sqrt{5}})$

Hence, option $\left(c\right)$ is correct.