The dome of an electrostatic generator is a spherical conductor of radius 13cm. It is initially charged so that the electric potential at the surface is 4.5kV. A smaller isolated sphere of radius 5.2cm, initially uncharged, is brought near to the dome. Sparking causes a current between the two spheres until they reach the same potential. Assume that any charge on a sphere may be considered to act as a point charge at its centre. Calculate the charge that is transferred between the two spheres.

1. (a)Define electric potential.[2]
2. (b)An isolated conducting sphere in a vacuum has radius r and is initially uncharged. It is then charged by friction so that it carries a final charge Q. This charge can be considered to be acting at the centre of the sphere. By considering the electric potential at its surface, show that the capacitance C of the sphere is given by C = 4πε₀r where ε₀ is the permittivity of free space.[2]
3. (c)The dome of an electrostatic generator is a spherical conductor of radius 13cm. It is initially charged so that the electric potential at the surface is 4.5kV. A smaller isolated sphere of radius 5.2cm, initially uncharged, is brought near to the dome. Sparking causes a current between the two spheres until they reach the same potential. Assume that any charge on a sphere may be considered to act as a point charge at its centre. Calculate the charge that is transferred between the two spheres.[3]