Question

A charge $Q$ is placed at each of the opposite corners of a square and charge $q$ is placed at each of the other two corners. If the net electrostatic force on $Q$ is zero, then $\frac{Q}{q}$ equals :-

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

Answer 1

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

$F_{net}$ on $q=\overline{F_1}+\overline{F_2}+\overline{F_3};o=F_i+F_j+\overline{F_3}$

$o=\frac{kq\theta }{a^2}(i+j)+\frac{k{q}^2}{\sqrt{2a^2}}\frac{i+j}{\sqrt{2}}$

$o=\frac{kq\theta }{a^2}+\frac{k{q}^2}{2\sqrt{2a^2}}(i+j)$

$q\theta +\frac{q^2}{2\sqrt{2}}=0\Rightarrow q=-2\sqrt{2}Q$