Question

Four charges, each equal to $-Q$, are placed at the corners of a square and a charge $+q$ is placed a the centre. if the system is in equilibrium, the value of $q$ is

• A. $0.25Q(1+2\sqrt{2})$
• B. $-0.25Q(1+2\sqrt{2})$
• C. $-0.5Q(1+2\sqrt{2})$
• D. $0.5Q(1+2\sqrt{2})$

Answer 1

The correct option is A $0.25Q(1+2\sqrt{2})$

Equating net force to be zero

$\frac{K2Qq}{{\left(a\right)}^2}=\frac{K{Q}^2}{{\left(a\right)}^2}\lceil \sqrt{2}+\frac{1}{2}\rceil q=0.25Q[1+2\sqrt{2}]$