PHY531 Problem Set 2. Due September 20, 2001.

- 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) - 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) 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. - 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)

(6) - Jackson Problem 1.23. Part c is not optional. Jackson's ``accurate'' numerical
values should be changed to
, ,
, and
.
- Jackson Problem 2.3
- Jackson Problem 2.5