Question

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

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

Answer 1

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

$\frac{Q}{q}=-2\sqrt{2}$

$F_{net}$ on $q={\overline{F}}_1+{\overline{F}}_2+{\overline{F}}_3$

$0=F\hat{i}+F\hat{j}+{\overline{F}}_3$

$0=\frac{K_{q}Q}{a^2}(\hat{i}+\hat{j})+\frac{{Kq}^2}{{\left(\sqrt{2}a\right)}^2}\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

$0=(\frac{K_{q}Q}{a^2}+\frac{K_{q}Q}{2\sqrt{2}{a}^2}(i+j))$

$qQ+\frac{a^2}{2\sqrt{2}}=0$

$q=-2\sqrt{2}Q$