Question

Four point charge $Q,q,2q$ 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

• A. $Q=-q$
• B. $Q=-\frac{1}{q}$
• C. $Q=q$
• D. $Q=\frac{1}{q}$

Answer 1

Answer: (A)

Let a be the side length of the square ABCD.
$ABCD\therefore AC=BD=\sqrt{a^2+a^2}=a\sqrt{2}$
$OA=OB=OC=OD=\frac{a\sqrt{2}}{2}=\frac{a}{\sqrt{2}}$ Potential is a scalar quantity.
Potential at the centre $O$ due to given charge configuration is
$V=\frac{1}{4\pi {\epsilon }_0}\left[\frac{(-Q)}{\frac{a}{\sqrt{2}}}+\frac{(-q)}{\frac{a}{\sqrt{2}}}+\frac{(2q)}{\frac{a}{\sqrt{2}}}+\frac{(2Q)}{\frac{a}{\sqrt{2}}}\right]=0$
$\Rightarrow -Q-q+2q+2Q=0$ or $Q+q=0$ or $Q=-q$