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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

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Solution

Since the two charges (spheres) attract, they will be opposite in sign, ie, q1 and –q2.
Force, F= k * q1 * q2/ d2
After touching, charge on each will be (q1 - q2)/2.
New force, F=k*[(q1 - q2)/2]2/ d2.
Since both the force are same(given in question)
So, on solving by quadratic equations, we get
q1/ q2 = -(3 + √(8)) or (-3 + √(8))

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