🚀 go-pugleaf

On March 25, 1995   David Thiessen <dtheissn@NSLSILUS.ORG> wrote:

> While my AP class was studying the magnetic force on an electric charge
> moving through a magnetic field, I made the statement that since the force
> was perpendicular to the velocity, the force could do no work on the moving
> charge.  It could change the direction of the velocity but not the speed
> and kinetic energy. Chris, who seems to immediately see universal
> consequences of my statement, raised his hand and asked, "If magnetic
> forces can do no work on moving charges, how can your big horseshoe magnet
> pick up a steel plate like you showed us?"
>
> My answer currently is (you may laugh but if you do, please send a better,
> more satisfying [?] explanation):  As the magnet is brought near the steel
> plate, there will be a changing magnetic flux through any chosen area
> inside the plate creating an electric field which will do work on the
> moving charges. Within the atom, the electron spins and orbital planes (?)
> will be re-oriented and, macroscopically, the magnetic domains will align
> in the external B field. This will result in attraction between the magnet
> and the steel plate ....

About 50 years ago this question would be answered with the magnetostatic
model (no longer in use). According to that model each magnet is a dipole
made from two "magnetic charges". A teacher would say (see old textbooks)
that domains are small magnets and that they orient their poles to be
attracted (disimilar magnetic poles attract). The model was originally
developed by Weber in the last decade of 19th century. Similar descriptions
are used to explain why pieces of paper are attracted by electic charges.

Today domains are viewed as current loops. A current loop in a UNIFORM
magnetic field only changes its orientation. But in a NONUNIFORM field
it is also attracted into the region in which the field is stronger. The
field of a horseshoe magnet is not uniform and the net force is produced
on a piece of iron in which the domains are located. A mathematical
calculation of the net force (as a funcion of distance x) is possible if
B(x) is given but this is not as simple as using the old "Coulomb's law
for magnetic poles".

To promote experimental physics I would suggest the following activity.
Using a magnetometer determine how the magnetic field, B, changes as a
function of the distance from the pole, x. Use as strong magnet as
possible. Then use a force-meter to measure F(x) on a small piece of iron.
Once this is done ask for the mathematical analysis of your specific
situation. A kid who is able to analytically describe the behavior of a
nonlinear oscillator (F=-k*x^n) should enjoy the task. I suspect that the
shape of the F(x) function can be calculated without knowing the permeability
of the iron used in the experiment. But I am not sure.

By the way, can you send me (on paper via snail-mail) the solution of
this nonlinear oscillator problem. I was working on it recently and solved
it numerically rather than analytically.

                  Ludwik Kowalski     kowalski@apollo.montcair.edu

  Physics at SMNS, Montcair State University, Upper Montclair, NJ, 07043