Question

Two identical conducting spheres carrying different charges attract each other with a force $F$ when placed in air medium at a distance $d$ apart. The spheres are brought into contact and then taken to their original positions. Now the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force. The ratio between initial charges on the spheres is

• A. $-\left(\right.3+\sqrt{8}\left.\right)$ only
• B. $-3+\sqrt{8}$ only
• C. $-\left(\right.3+\sqrt{8}\left.\right)$ or ( $-3+\sqrt{8}$ )
• D. $-\sqrt{8}$

Answer 1

Answer: (C)

$F= \, \frac{k q_{1} q_{2}}{d^{2}}$
After touching $\textit{F'}= \, \frac{k}{\left(\textit{d}\right)^{2}}\left(\frac{\left(\textit{q}\right)_{1} - q_{2}}{2}\right)^{2}$
$F \, =F'$
$q_{1}q_{2} \, = \, \left(\frac{q_{1} - q_{2}}{2}\right)^{2}$
$\frac{q_{1}}{q_{2}} \, = \, - \, 3 \, + \, \sqrt{8} \, or \, - \, 3 \, - \, \sqrt{8}$