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

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Question

$A$ is the midpoint

of $PS$

${	herefore \quad PA = AS = L}$

${AR = AQ = \sqrt {{{(SR)}^2} + {{(AS)}^2}} }$

${ = \sqrt {{{(2L)}^2} + {{(L)

Vedclass · Accepted Answer

$\;\frac{1}{{4\pi {\varepsilon _0}}}\frac{{2q}}{L}\left( {1 - \frac{1}{{\sqrt 5 }}} \right)$

Vedclass · Answer

$A$ is the midpoint

of $PS$

${	herefore \quad PA = AS = L}$

${AR = AQ = \sqrt {{{(SR)}^2} + {{(AS)}^2}} }$

${ = \sqrt {{{(2L)}^2} + {{(L)}^2}}  = L\sqrt 5 }$

Electric potential at point $A$ due to the given charge configuration is

$V_{A} =\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q}{P A}+\frac{q}{A S}+\frac{(-q)}{A Q}+\frac{(-q)}{A R}ight]$

$=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q}{L}+\frac{q}{L}-\frac{q}{L \sqrt{5}}-\frac{q}{L \sqrt{5}}ight]$

$=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{2 q}{L}-\frac{2 q}{L \sqrt{5}}ight]=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L}\left[1-\frac{1}{\sqrt{5}}ight]$

Four electric charges $+q,+q, -q$ and $-q$ are placed at the comers 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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