Physics 341 HW27

Due Monday, 27 November 2017

All of the below problems require that you use “Ampère’s Law for ”. I included a problem for each type of symmetry that can be done with this technique. In all problems below, s is the usual cylindrical coordinate (perpendicular distance from the z axis) and k is a constant.

  1. A very long, straight cylindrical wire of radius R lies with its axis on the z-axis. It carries a free current density . Using “Ampère’s Law for ”, determine expressions for inside and outside the wire.
  1. A very long, wide slab with thickness 2d lies with its faces parallel to the xy plane and the xy plane cutting through its center. It carries a free current density . Using “Ampère’s Law for ”, determine expressions for inside and outside the slab.
  1. A very long, straight cylinder with radius R lies with its axis on the z-axis. It carries a uniform surface current density where Ko is a constant. Determine, using the usual method of applying Ampère’s Law to a solenoid (see in-class notes from 8 Nov. or Griffiths ppg. 235-7), expressions for inside and outside the cylinder. (NOTE: You should also try this same problem only with a inside the cylinder either in place of or in combination with the surface current.)
  1. A toroid with a square cross-sectionlies with the z-axis going through the middle of the hole perpendicular the the “plane” of the donut. Its inner radius is a, its outer radius is b, and its thickness is 2t. It carries a current on its surface. The “upper” surface (a circular ring in the z = +t plane) carries a surface current, while the “lower” surface (a circular ring in the z = -t plane) carries a surface current . The outside surface (a circular strip at s = b) carries a surface current while the inner surface (a circular strip at s = a) carries a surface current . Using “Ampère’s Law for ”, determine expressions for inside and outside the toroid.