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Re: [Phys-l] magnetic forces & potential energy

Alas the far field calculations are not relevant because a motor uses the near field. One can treat the poles as point poles and have a model for the forces which resembles Coulomb's law. This should work much better for the near field than looking at dipole moments. It is not exact, but it should be conceptually understandable by HS students. The students would have to measure the forces to find the necessary parameters. F = constant x S1 S2/r^2, where the S is the pole strength. The potential energy would go as -1/r^3. The students would then have to remember to calcluate both poles separately.

John M. Clement
Houston, TX


As to your question about the potential energy: Again for the case of
two magnets whose dimensions are so small compared to their separation
that we can treat the magnets as point particles each of which has a
magnetic dipole moment; again we need to determine (again see Ch 17 of
Calculus-Based Physics II) the magnetic field of one of the magnets
(call it the source magnet) at the location of the other magnet (call it
the victim magnet), and this time we express the potential energy of the
system as
- mu dot B

where the vector mu is the magnetic dipole moment of the victim magnet
and the vector B is the magnetic field of the source magnet at the
location of the victim magnet.

Imagine moving the victim magnet a fixed-sized tiny step in each of many
different directions in turn, always from the original location, without
turning the magnet. The direction in which taking the tiny step results
in the greatest increase in mu dot B is the direction of the force
exerted on the magnet. Just as the torque exerted on the magnet is in
that sense of rotation, which tends to maximize mu dot B, the force on
the magnet, when it is in a non-uniform magnetic field is in that
direction which tends to maximize mu dot B [or minimize the potential
energy (- mu dot B) if you prefer].

Example

Consider a horizontal bar magnet, to the right of a long straight
horizontal wire carrying a steady current right at you, where the bar
magnet is pointing leftward (think of the bar magnet as an arrow, with
the north pole being the arrowhead--that arrow also represents the
magnetic dipole moment of the magnet) straight at the wire.

The magnetic field of the wire, at the location of the bar magnet is
upward, and in the overall region, the magnetic field is in the form of
circles directed counterclockwise around the wire from your viewpoint.

The dot product mu dot B is zero because mu is perpendicular to B and
the dot product remains zero, for the same reason, if you move the
magnet a tiny step toward or away from the wire (without allowing the
magnet to turn). Likewise for a tiny step along the wire, either toward
or away from you. So the force on the magnet has no component in the
toward-the-wire direction and it has no component in the
parallel-to-the-wire direction. But if you were to move the magnet a
tiny step upward, the magnet will find itself at a point in space at
which the magnetic field has a (tiny) leftward component meaning that
the dot product mu dot B would increase to some positive value (from
zero) as a result of the hypothetical tiny step upward. This means that
at the original location of the bar magnet, the bar magnet is
experiencing an upward force. This is consistent with the
leftward-directed magnetic field of the bar magnet, at the location of
the wire, exerting a downward F = I L cross B force on the wire.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Paul Lulai
Sent: Wednesday, May 14, 2008 11:55 AM
To: Forum for Physics Educators
Subject: [Phys-l] magnetic forces & potential energy

Hello.

I have a student that is trying to design an electric motor. I know
there are a million different (& easy) electric motor designs
available.
He is trying something a bit unique.

The student has magnets that state they have a 'strength' of 200
pounds.
I believe that this is the force of attraction btn the magnet and a
ferromagnetic substance when the two are in contact. Is there a high
school method (algebra or calc 1 method) that would make it possible
to
calculate:
1- the force of attraction btn two magnets (one electromagnet & one
permanent magnet) when they are separated by some distance?
2- the potential energy of a two magnet system in which the two
magnets
are separated?

Your help is appreciated. I haven't used much of my e&m since I took
the course. It appears I've forgotten quite a bit. A bit shameful.

Thanks for your input.

Paul Lulai . . . To wonder is to begin to understand
Physics Instructor
Science Olympiad Coach
US First Robotics Teacher
.: Medtronic - St Anthony RoboHuskie Team 2574:.
Saint Anthony Village Senior High School, ISD 282
3303 33rd Avenue N.E.
Saint Anthony Village, MN 55418
(w) 612-706-1144
(fax) 612-706-1140

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