Q. Four point charges $-Q, -q, 2q$ and $2Q$ 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 :
BITSATBITSAT 2018
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 $
$\Rightarrow +q=0$ (Given)
$Q=-q$
