Question

Charges $Q$ are placed at the ends of a diagonal of a square and charges $q$ are placed at the other two corners. The condition for the net electric force on $Q$ to be zero is

• A. $Q=-2 \sqrt{2} q, q$ being negative
• B. $Q=-\frac{q}{2}, q$ being negative
• C. $Q=2 \sqrt{2} q, q$ being negative
• D. $Q=2 q, q$ being negative

Answer 1

Answer: (A)

Net force on $D$ due to $A$ and $B=\frac{K \sqrt{2} Q q}{a^{2}}$

Force on $D$ due to $B=\frac{K Q^{2}}{2 a^{2}}$
For net electric field on $D$ to be zero
$K\left[\frac{Q^{2}}{2 a^{2}}+\frac{\sqrt{2} Q q}{a^{2}}\right]=0$
$\Rightarrow \frac{Q}{2}+\sqrt{2} q=0$
$Q=-2 \sqrt{2} q$
$\therefore q$ should be negative.