Two identical conducting spheres, having charges of opposite sign, attract each other with a force of 0.108 N when separated by 50.0 cm. The spheres are suddenly connected by a thin conducting wire, which is then removed, and thereafter spheres repel each other with a force of 0.0360 N. We have to find the initial charges on the spheres.

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Let the initial charges on the two conducting spheres be and , respectively. Each conducting sphere will attract the other with a force of magnitude

It is given that

Let .

When the conducting spheres are connected by a thin conducting wire, charge will flow from one to the other till the charge on each conducting sphere becomes .

It is given that when the conducting wire is removed, the two conducting spheres repel each other with a force

From the Coulomb’s law, we have the equation

We find

We have also found that

Using the identity

We get

From the above results, we get