MAGNETIC FORCES, MATERIALS,
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Having considered the basic laws and techniques commonly used in calculating magnetic
field B due to current-carrying elements, we are prepared to study the force a magnetic
field exerts on charged particles, current elements, and loops. Such a study is important to
problems on electrical devices such as ammeters, voltmeters, galvanometers, cyclotrons,
plasmas, motors, and magnetohydrodynamic generators. The precise definition of the mag-
netic field, deliberately sidestepped in the previous chapter, will be given here. The con-
cepts of magnetic moments and dipole will also be considered.
Furthermore, we will consider magnetic fields in material media, as opposed to the
magnetic fields in vacuum or free space examined in the previous chapter. The results of
the preceding chapter need only some modification to account for the presence of materi-
als in a magnetic field. Further discussions will cover inductors, inductances, magnetic
energy, and magnetic circuits.
8.2 FORCES DUE
There are at least three ways in which force due to magnetic fields can be experienced. The
force can be (a) due to a moving charged particle in a B field, (b) on a current element in an
external B field, or (c) between two current elements.