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. $Q=2q,q$ being negative

Answer 1

Answer: (A)

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

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