Question

Four point charges $-Q,-q,2q$ and $2Q$ are placed, at different corners of a square. The relation between $-Q$ and $q$ for which the potential at the center of the square is zero is:-

• A. $Q=q$
• B. $Q=1/q$
• C. $Q=-q$
• D. $Q=-1/q$

Answer 1

The correct option is C $Q=-q$


$O$ is the centre of the square.

So, distacne $\text{BO}$ is

$r=\sqrt{a^2+a^2}=a\sqrt{2}$

So, net potential at the centre $O$ of square is given by

$V_O=-\frac{KQ}{r}-\frac{Kq}{r}+\frac{2Kq}{r}+\frac{2KQ}{r}$

Given: $V_O=0$

$\therefore 0=-\frac{KQ}{r}-\frac{Kq}{r}+\frac{2Kq}{r}+\frac{2KQ}{r}$

$\Rightarrow Q+q=2Q+2q$

$\Rightarrow Q=-q$

Hence, option $\left(c\right)$ is correct.