Four electric charges +q, +q, -q and -q are p | vedclass

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(C) Let the corners of the square be $P, Q, R, S$ in order. Let $P$ and $S$ have charges $+q$,and $Q$ and $R$ have charges $-q$. Point $A$ is the midp

Vedclass · Accepted Answer

$\frac{1}{4\pi \varepsilon_0} \frac{2q}{L} (1 - \frac{1}{\sqrt{5}})$

Vedclass · Answer

(C) Let the corners of the square be $P, Q, R, S$ in order. Let $P$ and $S$ have charges $+q$,and $Q$ and $R$ have charges $-q$. Point $A$ is the midpoint of side $PS$.Since the side length is $2L$,the distance from $A$ to $P$ and $A$ to $S$ is $L$.The distance from $A$ to $Q$ and $A$ to $R$ can be calculated using the Pythagorean theorem: $AQ = AR = \sqrt{(2L)^2 + L^2} = \sqrt{4L^2 + L^2} = L\sqrt{5}$.The electric potential $V_A$ at point $A$ is the algebraic sum of potentials due to all four charges:$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{q}{AP} + \frac{q}{AS} + \frac{-q}{AQ} + \frac{-q}{AR}]$$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{q}{L} + \frac{q}{L} - \frac{q}{L\sqrt{5}} - \frac{q}{L\sqrt{5}}]$$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{2q}{L} - \frac{2q}{L\sqrt{5}}]$$V_A = \frac{1}{4\pi \varepsilon_0} \frac{2q}{L} (1 - \frac{1}{\sqrt{5}})$

Four electric charges $+q, +q, -q$ and $-q$ are placed at the corners of a square of side $2L$ (see figure). The electric potential at point $A$,midway between the two charges $+q$ and $+q$,is

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