Question

A charge $Q_1$ is placed at each of two opposite corners of a square. A charge $Q_2$ is placed at each of the other two corners. If the net electric force on $Q_1$ is zero, then $Q_1/Q_2$ equals:

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

Answer 1

The correct option is D $-2\sqrt{2}$

The net force on $Q_1$ is given as,

$0={\overrightarrow{F}}_1+{\overrightarrow{F}}_2+{\overrightarrow{F}}_3$

$0=\frac{k{Q}_1{Q}_2}{a^2}\left(\hat{i}+\hat{j}\right)+\frac{k{Q_1}^2}{{\left(\sqrt{2}a\right)}^2}\frac{\left(\hat{i}+\hat{j}\right)}{\sqrt{2}}$

$0=\left(\frac{k{Q}_1{Q}_2}{a^2}+\frac{k{Q_1}^2}{\left(2\sqrt{2}{a}^2\right)}\right)\left(\hat{i}+\hat{j}\right)$

$0=\left(Q_1{Q}_2+\frac{{Q_1}^2}{\left(2\sqrt{2}\right)}\right)$

$\frac{Q_1}{Q_2}=-2\sqrt{2}$