Question

It is required to hold equal charges $q$ in equilibrium at the corners of a square. What charge when placed at the center of the square will do this?

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

Answer 1

Answer: (D)

$A C=\sqrt{2} l=B D $
or $B O=\frac{1}{\sqrt{2}}$

$F_{B O}=F_{B D}+\left(F_{B A}+F_{B C}\right) \cos 45^{\circ}$.
Solving, we get
$Q=\frac{q}{4}(1+2 \sqrt{2})$ and $Q$ should be negative of $q .$