Page 311 - Electrical Properties of Materials
P. 311
Exercises 293
they were supplanted by another magnetoresistive effect based on tunnelling,
as discussed in Section 11.11.2.
11.12.4 Electric motors
This is one of the oldest applications of magnetism, the conversion of elec-
trical into mechanical power. Have there been any major advances? Well, our
illustration of what happened to the magnetic circuit of moving-coil meters
(Fig. 11.13) applies just as well to electric motors. They have come down in
size, so much so that in a modern motor car there is room for as many as
two dozen permanent magnet motors, which drive practically everything that
moves (apart from the car, of course).
Some forty years ago, all the electric motors that we moved about the labor-
1
atory or our homes were ‘fractional horse power’. In fact, a h.p. motor was
2
rather large and heavy. Anything greater than 1 h.p. was classed as ‘industrial’
and had a built-in fan or water cooling. Now our domestic motors are smaller,
cooler, and quieter; and where power is needed, such as in portable drills, lawn-
mowers, and shredders, ratings of up to 1.6 kW (i.e. more than 2 h.p.) are quite
common and reasonably portable. What has happened besides the discovery
of better magnetic alloys? This is something we should have mentioned in the
last chapter in the section about insulators. The makers of motors woke up to
the fact that new polymeric insulations were available that were more effective
than the brown paper soaked in transformer oil which they had been using for
the previous century. I am telling you this story because it illustrates that some
improvements in technology, which the public is hardly aware of, can have a
significant impact upon how we live.
Exercises
11.1. Check whether eqn (11.12) is dimensionally correct. (iii) Confirm that in the stable equilibrium position the mag-
Take reasonable values for N a , Z and r and calculate the order netic field of the loop augments the applied field.
of magnitude of the diamagnetic susceptibility in solids.
I
11.2. The magnetic moment of an electron in the ground
state of the hydrogen atom is 1 Bohr magneton. Calculate the
induced magnetic moment in a field of 1 T. Compare the two.
11.3. A magnetic flux density, B, is applied at an angle θ θ
to the normal of the plane of a rectangular current loop I
(Fig. 11.33).
B
(i) Determine the energy of the loop by finding the work
done by the magnetic field when lining up (bringing to a Fig. 11.33
stable equilibrium) the loop. 11.4. How have domains in ferromagnetic materials been
(ii) By defining the energy of a magnetic dipole as observed?
E = μ m · B,
11.5. Check the calculation leading to the values of the Weiss
and by identifying the loop with a magnetic dipole, constant, magnetic moment, and saturation magnetization for
determine the magnetic moment vector of the loop. iron given in eqn (11.28).