Problems in Magnetism (not in the typical phys book)
(Make some reasonable assumptions to solve these.)

  1. A long bar magnet has pole area A. An identical magnet is brought up close to the first so that a pair of opposite poles are parallel and almost touching. The magnetic field between them is B. Find the force of attraction.
  2. A long thin cylindrical bar magnet, length L and radius r, has magnetic field Bo at its poles. Find its dipole moment. (Note: if this were an air-core coil, the dipole moment would be NIp r2.)
  3. A cylindrical magnet has radius r, length 4r, and magnetic field Bo at the poles. Find the magnetic field a distance 2r from the end on the axis of the cylinder.

With the magnet in problem 2, find the field at a point that forms the right angle corner of a 3-4-5 triangle with the magnet as the hypotenuse.

Answers (which might even be correct) Don't peek!

  1. F = AB2/2m o
  2. m B = 2LBo p r2/m o
  3. B = 0.095Bo
  4. B = 3.2Bor2/L2 at an angle of 29o or 61o outside the triangle, measured from the line to the south pole (the smaller angle if S is the closer pole), or if you prefer, 24o relative to the magnet.

Reasonable assumptions

    1. Assume constant B over area A; B small elsewhere (like the parallel-plate capacitor assumption). Energy/volume in B field is B2/2m o.
    2. Assume that it has the same magnetic moment as a long coil that is producing the same Bo at its end.
    3. Assume that the field is the same as the field of coil that has field Bo at its end.
    4. Assume that it acts like the electric field due to oppositely charged spheres of radius r, long distance L apart, so Eo = (1/4p e o)q/r2 at a sphere surface.

Go back to the main E&M page where you can find solutions if you wish, and other things, some of them halfway useful.

My main pages:

mechanics
fluids, heat, electricity and magnetism
vibrations and waves
quantum

Comments, questions: fredrick.gram@tri-c.edu