Four point charges $-Q, -q, 2q$ and $2Q$ are placed, one at each comer of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is
AIPMT 2012, Medium
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Let the distance of the center from each corner be $a$ . The the potential at the center is
$V = \frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{{ - Q}}{a} + \frac{{ - q}}{a} + \frac{{2q}}{a} + \frac{{2Q}}{a}} \right)$$ = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{Q + q}}{a}$
This is zero if
$Q+q=0$
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