Question

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then the $Q/q$ equals

• A. $-2\sqrt{2}$
• B. $-1$
• C. $1$
• D. $-\frac{1}{\sqrt{2}}$

Answer 1

Answer: (A)

Three forces $F_{41},F_{42}$ and $f_{43}$ acting on $Q$ are shown Resultant of $F_{41}+F_{43}$
$=\sqrt{2}{F}_{each}$
$=\sqrt{2}\frac{1}{4\pi {\epsilon }_o}\frac{Qq}{d^2}$
Resultant on Q becomes zero only when ‘q’ charges are of negative nature.
$F_{4,2}=\frac{1}{4\pi {\epsilon }_o}\frac{Q\times Q}{{\left(\sqrt{2}d\right)}^2}$
$\Rightarrow \sqrt{2}\frac{dQ}{d^2}=\frac{Q\times Q}{2}$
$\Rightarrow \sqrt{2}\times q=\frac{Q\times Q}{2}$
$\therefore q=-\frac{Q}{2\sqrt{2}}$ or $\frac{Q}{q}=-2\sqrt{2}$