A solid copper sphere whose radius is 1.0 cm has a very thin surface coating of nickel. Some of the nickel atoms are radioactive, each atom emitting an electron as it decays. Half of these electrons enter the copper sphere, each depositing 100keV of energy there. The other half of the electrons escape, each carrying away a charge – e the nickel coating has an activity of 3.70 x 108 radioactive decays per second. The sphere is hung from a long, non-conducting string and isolated from its surroundings.

(a) How long will it take for the potential of the sphere to increase by 1000 V?

(b) How long will it take for the temperature of the sphere to increase by 5.0 K due to the energy deposited by the electrons the heat capacity of the sphere is 14J/K.