Electrostatics problem

[kolahal_b]

1]Two small spheres, each of mass m, are suspended from the same point by silk threads of length l. The distance between the spheres x<<l. Find the rate dq/dt with which the charge leaks off each sphere if their approach velocity varies as v=a√x, where a is a constant.

The problem has been done: First we find q2 in equilbm Condition in terms of m, g, l, x etc. Then we differentiate w. r. t. time. dq/dt may be obtained from this. But I wonder why will the charge leakage occur?What feature of the problem is responsible for the charge leakage to occur?

2] A thin wire ring of radius R has an electric charge q. What will be the increment in the force stretching the wire if a point charge q0 is placed at the ring’s center?

This is a typical one. What I feel, when we have not introduced the point charge inside the ring, the E field was distributed inside and outside the ring in its way. The resultant E field at the center was nil. When we put the point charge at the center, the pattern redistributes to most stable configuration. If the charge in the ring and the point charge are of same sign, the field somewhat cancels out within the ring and rebuilds itself outside the ring. The difference in the force in the inside wall and the outside wall of the ring makes the ring to tend to expand. Our aim is to find the difference of the two forces.

It appeared to me difficult to find directly the E field. Instead, I tried to find the potential due to the charged ring and the point charge. Once we get the total potential, we also get E field. But the integration to find potential turns out to be hopelessly difficult. Please help.

Kolahal Bhattacharya.

[Tormod]

Closed since this has also been posted in the Phsycs forum.