Question

Four charges each equal to $Q$ are placed at the four corners of a square and a charge $q$ is placed at the centre of the square. If the system is in equilibrium then the value of $q$ is

• A. $\frac{Q}{2}(1+2\sqrt{2})$
• B. $\frac{-Q}{4}(1+2\sqrt{2})$
• C. $\frac{Q}{4}(1+2\sqrt{2})$
• D. $\frac{-Q}{2}(1+2\sqrt{2})$

Answer 1

Answer: (B)

Net force on $Q$ due to other corner charge is
$F_{123}=F_3+\sqrt{F_1^2+F_2^2}$
$=F_3+\sqrt{2}{F}_1$
$=\frac{K{Q}^2}{2l^2}+\frac{\sqrt{2}K{Q}^2}{l^2}$
Force on $Q_1$ due to centre charge $-q$
$F_4=\frac{KQq}{I^2}.2$
If net force on corner charge $Q$ is zero Then
$F_{123}+F_4=0$
So $q=-\frac{Q}{4}[1+2\sqrt{2}]$