Problems in Magnetism (not in the
typical phys book)
(Make some reasonable assumptions to solve these.)
- 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.
- 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.)
- 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!
- F = AB2/2m o
- m B = 2LBo p r2/m o
- B = 0.095Bo
- 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
- Assume constant B over
area A; B small elsewhere (like the parallel-plate capacitor assumption).
Energy/volume in B field is B2/2m
o.
- Assume that it has the
same magnetic moment as a long coil that is producing the same Bo
at its end.
- Assume that the field
is the same as the field of coil that has field Bo at its end.
- 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