A conducting sphere S1 of radius r is attached to an insulating handle. Another conducting sphere S2 of radius R is mounted on an insulating stand S2 is initially uncharged.
S1 is given a charge Q brought into contact with S2 and removed. This procedure is repeated n times.
1. Find the electrostatic energy of S2after n such contacts with S1.
2. What is the limiting valve of this energy as n →∞ ?
3. A particle of mass m and charge q is moving in a region where uniform constant electric and magnetic fields E and B are present. E and B are parallel to each other. At time t = 0, the velocity v0 of the particle is perpendicular to E (Assume that its speed is always << c, the speed of light in vacuum). Find the velocity v of the particle at time t. [You must express your answer in terms of t, q, m, the vectors v0, E an B and their magnitudes v0, E and B.
Suorce 1998 JEE