Four point charges $-Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of the square. The relation between $Q$ and $q$ for which the potential at the centre of the square is zero is

• Correct answer
  A

  $Q=-q$
• B

  $Q=-\frac{1}{q}$
• C

  $Q=q$
• D

  $Q=\frac{1}{q}$

Solution

Let the side length of square be ' $a$ ' then potential at centre $O$ is $V=\frac{k(-Q)}{\left(\frac{a}{\sqrt{2}}\right)}+\frac{k(-q)}{\frac{a}{\sqrt{2}}}+\frac{k(2 q)}{\frac{a}{\sqrt{2}}}+\frac{k(2 Q)}{\frac{a}{\sqrt{2}}}=0$
$=-Q-q+2 q+2 Q=0 \Rightarrow Q+q=0$ $\Rightarrow Q=-q$

Hence, the correct answer is option: 'A'.