Question

Four charges $100\mu C,-50\mu C,20\mu C$ and $-60\mu C$ are placed at the corners of a square of side $\sqrt{2}m$.Calculate the electric potential at the centre of the square.

Answer 1

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
$\begin{array}{c}{V}_0=\frac{k{q}_1}{AO}+\frac{k{q}_2}{BO}+\frac{k{q}_3}{CO}+\frac{k{q}_4}{DO}\\ V_0=\frac{k}{1}[100-50+20-60]\times {10}^{-6}\\ V_0=9\times {10}^9[10\times {10}^{-6}C]\\ V_0=9\times {10}^9\times 10\times {10}^{-6}volt\\ V_0=9\times {10}^4\text{volt}\end{array}$