Problems from HRW Problem Supplement #1 (6th edition)
Chapter 30

73.  A long, hollow cylindrical conductor (inner radius
     = 2.0 mm, outer radius = 4.0 mm) carries a current
     of 24 A distributed uniformly across its cross
     section.  A long thin wire that is coaxial with
     the cylinder carries a current of 24 A in the 
     opposite direction.  What are the magnitudes of 
     the magnetic fields (a) 1.0 mm, (b) 3.0 mm, and
     (c) 5.0 mm from the central axis of the wire and
     cylinder?

74.  Show that if the thickness of a toroid is very
     small compared to its radius of curvature (a very
     skinny toroid), then Eq. 30-26 for the field 
     inside a toroid reduces to Eq. 30-25 for the field
     inside a solenoid.  Explain why this result is to
     be expected.

Problems from Fishbane, Gasiorowicz, and Thornton
(2nd edition) Chapter 30

30.  Show that the magnetic flux through an ideal
     cylindrical solenoid of radius R is given by
     Phi_B = (mu_0)nI(pi)R²,where n is the
     turn density.

32.  Consider a toroidal solenoid with a square cross
     section, each side of which has length 3 cm.
     The inner wall of the torus forms a cylinder of
     radius 12 cm.  The torus is wound evenly with
     200 turns of 0.3 mm-DIAMETER copper wire.  The
     wire is connected to a 3.0 V battery with 
     negligible internal resistance.  (a) Calculate
     the largest and smallest magnetic field across
     the cross section of the toroid.  (b) Calculate
     the magnetic flux through the torus.  (c) Do
     you need to cool the solenoid?  (Calculate the
     heat created per second when current is flowing.)