Question

Four charges equal to q are placed at the four corners of a rectangle of side a and $b(a\ne b)$ and a charge Q is at its centre. If the system is in equilibrium, then the value of Q is:

• A. $-\frac{q}{4}(1+2\sqrt{2})$
• B. $\frac{-q}{2}\left[\frac{a+b+\sqrt{a^2+b^2}}{\sqrt{a^2+b^2}}\right]$
• C. $-q$
• D. This system will never be in equilibrium

Answer 1

The correct option is D This system will never be in equilibrium

$F_1>F_2(\because b<a)$

So, net force due to $F_{1}and{F}_2$ is more tilted towards $F_1$ as shown in diagram. So it is impossible to attain equilibrium with any value of Q.