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.
$ABCD \therefore A C=B D=\sqrt{a^{2}+a^{2}}=a \sqrt{2}$
$O A=O B=O C=O D=\frac{a \sqrt{2}}{2}=\frac{a}{\sqrt{2}}$ Potential is a scalar quantity.
Potential at the centre $O$ due to given charge configuration is
$V=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{(-Q)}{\frac{a}{\sqrt{2}}}+\frac{(-q)}{\frac{a}{\sqrt{2}}}+\frac{(2 q)}{\frac{a}{\sqrt{2}}}+\frac{(2 Q)}{\frac{a}{\sqrt{2}}}\right]=0$
$\Rightarrow -Q-q+2 q+2 Q=0$ or $Q+q=0$ or $Q=-q$