question_answer

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)        \[Q=\frac{1}{q}\]

Correct Answer: A

Solution :

If potential at centre is zero, then \[{{V}_{1}}+{{V}_{2}}+{{V}_{3}}+{{V}_{4}}=0\] \[-\frac{kQ}{r}-\frac{kq}{r}+\frac{k2Q}{r}+\frac{k2q}{r}=0\]                 \[-Q-q+2q+2Q=0\]                                                 \[Q=-q\]