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 with 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. $–(3 + \sqrt{8})$ only
• B. $–3 + \sqrt{8}$only
• C. $–(3 + \sqrt{8})$ or ($–3 + \sqrt{8}$)
• D. –$\sqrt{8}$

Answer 1

Answer: (C)

$–(3 + \sqrt{8})$ or ($–3 + \sqrt{8}$)

Answer 2

F =

After touching F ¢ = $\frac { \mathrm { K } } { \mathrm { d } ^ { 2 } } \frac { \left( \mathrm { q } _ { 1 } - \mathrm { q } _ { 2 } \right) ^ { 2 } } { 2 }$

F = F ¢

q₁q₂ =

$\frac { \mathrm { q } _ { 1 } } { \mathrm { q } _ { 2 } }$ = – 3 + $\sqrt { 8 }$ or – 3 – $\sqrt { 8 }$