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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