Question1

Reduce equations of motion to an equivalent one-dimensional problem and discuss qualitative nature of the orbit for different values of the energy. For bound orbits, show that the particle takes a nite length of time to spiral into the center of force, passing through a nite number of revolutions.

Question2

Consider two conducting spheres with radii R1 and R2 separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a least value, potential difference between the spheres is zero. The total charge Q is equal to q1 + q2, where q1 represents the charge on the first sphere and q2 the charge on the second. While the spheres are very far apart, you can assume charge of each is uniformly distributed over its surface.