PHY531 Problem Set 2. Due September 20, 2001.

1. The work required to bring a point charge up to the centers, which are a distance apart, of two thin parallel conducting coaxial rings, each of radius , is and , respectively. Show that the charges on the rings are
 (1)

.

2. Two parallel coaxial circular rings of radii and carry uniformly distributed charges and . The distance between their planes is . Show that the force between them is
 (2)

and is a complete elliptic integral of the second kind of modulus .

The complete elliptic integrals with are defined in Abramowitz and Stegun chapter 17 as

 (3)

Complete reduction techniques are found there. You may find the derivative formulas
 (4)

useful.

3. A grounded conducting sphere of radius has its center on the axis of a charged circular ring with total charge . Any radius vector of length from its center to the ring makes an angle with the axis. Show that the force sucking the sphere into the ring is
 (5)

where
 (6)

and a complete elliptic integral of the second kind.

4. Jackson Problem 1.23. Part c is not optional. Jackson's accurate'' numerical values should be changed to , , , and .

5. Jackson Problem 2.3

6. Jackson Problem 2.5