Question

A large insulated sphere of radius r cagreged with Q units of electricity is placed in contact with a small insulated uncharged sphere of radius r' and is then separated. The charge on smaller sphere will now be

Answer 1

When brought in contact, the charge Q is distributed uniformly in both the spheres.

So, charge Q is distributed in volume, V = (4/3)Ï€r³ + (4/3)Ï€R³

=> V = (4/3)Ï€(r³ + R³)

So, volume charge density of the combination is, ρ = Q/V = Q/[(4/3)Ï€(r³ + R³)]

When they are separated, the charge remained on small sphere is, q = ρ × (4/3)Ï€r³

=> q = Q/[(4/3)Ï€(r³ + R³)] × (4/3)Ï€r³

=> q = Qr³/(r³ + R³)