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)

$-2\sqrt{2}$

Answer 2

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