Four point charges $-Q,-q, 2 q$ and $2 Q$ are placed, one at each corner of the square. The relation between…

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
  1. $Q=-q$
  2. $Q=-\frac{1}{q}$
  3. $Q=q$
  4. $Q=\frac{1}{q}$

Solution


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

Asked in: NEET 2012 (Screening)

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