Problems from HRW Problem Supplement #1 (6th edition)
Chapter 25

58.  Consider a flat, nonconducting ring of outer
     radius R and inner radius r = 0.200R;  the ring 
     has a uniform charge per unit area of sigma.
     With V = 0 at infinity, find an expression for
     the electric potential at point P on the central
     axis of the ring, at a distance z = 2.00R from 
     the center of the ring.

81.  In the quark model of fundamental particles, a
     proton is composed of three quarks: two "up"
     quarks, each having charge +2e/3, and one
     "down" quark, having charge -e/3.  Suppose that
     the three quarks are equidistant from one 
     another.  Take the distance to be 1.32 x 10^{-15} m
     and calculate (a) the electric potential energy 
     of the subsystem of two "up" quarks and
     (b) the total electric potential energy of the
     three-quark system.

88.  Three particles with the same charge q and same
     mass m are initially fixed in place to form an
     equilateral triangle with edge lengths d. 
     (a) If the particles are released simultaneously,
     what are their speeds when they have traveled a 
     large distance (effectively an infinite distance)
     from each other?  (Measure the speeds in the
     original rest frame of the particles.)

     Suppose, instead, the particles are released one
     at a time:  The first one is released, and then,
     when the first one is at a large distance, a
     second one is released, and then, when that second
     one is at a large distance, the last one is 
     released.  What then are the final speeds of
     (b) the first particle, (c) the second particle,
     and (d) the last particle?