Question

Four charges and are placed at the corners of a square of side .Calculate the electric potential at the centre of the square.

Medium

Solution

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According to figure Diagonal of square
$$\begin{aligned}(A C)^{2} &=(B D)^{2}=(\sqrt{2})^{2}+(\sqrt{2})^{2} \\
(A C)^{2} &=(B D)^{2}=2+2 \\ (A C) &=(B D)=\sqrt{4} \\ (A C) &=(B D)=2 \\A O &=B O=C O=D O=\dfrac{A C}{2} \\A O &=B O=C O=D O=1m, \dfrac{1}{4 \pi \varepsilon_0}=k\end{aligned}$$
Potential at the centre of square

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