Identical charges $(-q)$ are placed at each corner of a cube of side ' $b$ ' then the electrical potential…

Identical charges $(-q)$ are placed at each corner of a cube of side ' $b$ ' then the electrical potential energy of charge (+ $q$ ) which is placed at the centre of cube will be:
  1. $\frac{-4 \sqrt{2} q^2}{\pi \varepsilon_0 b}$
  2. $\frac{-8 \sqrt{2} q^2}{\pi \varepsilon_0 b}$
  3. $\frac{-4 q^2}{\sqrt{3} \pi \varepsilon_0 b}$
  4. $\frac{8 \sqrt{2} q^2}{4 \pi \varepsilon_0 b}$

Solution

Distance between the charge $-q$ and $+q$ is $r=\sqrt{\frac{(\sqrt{2} b)^2+(b)^2}{2}}=\frac{\sqrt{3}}{2} b$ Electric potential energy of charge $\begin{aligned} & +q \text { is } v=8 \times \frac{1}{4 \pi \varepsilon_0} \frac{q(-q)}{r} \\ & =8 \times \frac{1}{4 \pi \varepsilon_0} \frac{q(-q)}{\frac{\sqrt{3}}{2} b} \\ & U=\frac{-4 q^2}{\sqrt{3 \pi \varepsilon_0 b}} \end{aligned}$

Asked in: NEET 2002

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