Q135 / 160 · TS EAMCET 2015 · Physics
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
- Correct answerA$Q=-2 \sqrt{2} q, q$ 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
Solution
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 $$ \begin{aligned} K\left[\frac{Q^2}{2 a^2}+\frac{\sqrt{2} Q q}{a^2}\right] & =0 \\ \Rightarrow \quad \frac{Q}{2}+\sqrt{2} q & =0 \\ Q & =-2 \sqrt{2} q \end{aligned} $$ $\therefore q$ should be negative.
Force on $D$ due to $B=\frac{K Q^2}{2 a^2}$ For net electric field on $D$ to be zero $$ \begin{aligned} K\left[\frac{Q^2}{2 a^2}+\frac{\sqrt{2} Q q}{a^2}\right] & =0 \\ \Rightarrow \quad \frac{Q}{2}+\sqrt{2} q & =0 \\ Q & =-2 \sqrt{2} q \end{aligned} $$ $\therefore q$ should be negative.
Hence, the correct answer is option: 'A'.