Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2 \mathrm{~L}$ (see…

Four electric charges $+q,+q,-q$ and $-q$ are placed at the corners of a square of side $2 \mathrm{~L}$ (see figure). The electric potential at point $A$, mid-way between the two charges $+q$ and $+q$, is
  1. $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}\left(1+\frac{1}{\sqrt{5}}\right)$
  2. $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}\left(1-\frac{1}{\sqrt{5}}\right)$
  3. zero
  4. $\frac{1}{4 \pi \varepsilon_0} \frac{2 q}{L}(1+\sqrt{5})$

Solution

$V=\frac{1}{4 \pi \varepsilon_0} \frac{q}{r}$ Here, $\begin{aligned} & V=2 V_{+\mathrm{ve}}+2 V_{\text {-ve }} \\ & V=\frac{1}{4 \pi \varepsilon_0}\left[\frac{2 q}{L}-\frac{2 q}{L \sqrt{5}}\right] \\ & V=\frac{2 q}{4 \pi \varepsilon_0 L}\left(1-\frac{1}{\sqrt{5}}\right) \end{aligned}$

Asked in: NEET 2011 (Screening)

Practice more Electrostatics questions on Aicharya