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2. Electric Potential and Capacitance
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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
A
$Q = - q$
B
$Q=-$$\;\frac{1}{q}$
C
$\;Q = q$
D
$Q=$$\frac{1}{q}$ $\;$
(AIPMT-2012)
Solution
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
$Q+q=0$
Standard 12
Physics
