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Question

Four charges 100μC,50μC,20μC and 60μC are placed at the corners of a square of side 2m.Calculate the electric potential at the centre of the square.

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Solution

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
V0=kq1AO+kq2BO+kq3CO+kq4DOV0=k1[10050+2060]×106V0=9×109[10×106C]V0=9×109×10×106voltV0=9×104 volt
1763123_1836186_ans_71e7dd4720034426a06ee27a8ad62eb7.png

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