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

If potential at centre is zero, then $\begin{aligned} V_1+V_2+V_3+V_4 & =0 \\ -\frac{k Q}{r}-\frac{k q}{r}+\frac{k 2 Q}{r}+\frac{k 2 q}{r} & =0 \\ -Q-q+2 q+2 Q & =0 \\ Q & =-q \end{aligned}$

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