Environmental Engineering Reference
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D
H
i
Figure 2.1
Magnetic field due to current
The magnitude of the magnetic field due to current may be quantified by
Amp`re's Law (Christopoulos, 1990). When the field due to current i in an infi-
nitely long, straight conductor is considered, application of Amp`re's Law leads to
a simple and very useful result. The magnetic field strength H of the field at a
distance D from the conductor, as illustrated in Figure 2.1, is given by
i
2 p D
H ¼
ð 2 : 1 Þ
The magnetic field strength describes the magnetic stress on the medium due
to current. The actual magnetic field reflects the permeability of the medium. In the
case of a vacuum, or a non-magnetic medium such as air, the field is described by
flux density B . Flux density is related to magnetic field strength by
B ¼ m 0 H
ð 2 : 2 Þ
where m 0 is the permeability of free space . When the medium is magnetic, the flux
density for a particular magnetic field strength will be much greater, and is given by
B ¼ m r m 0 H
ð 2 : 3 Þ
where m r is the relative permeability of the magnetic material. Obviously, non-
magnetic materials have a relative permeability of 1. Ferromagnetic materials have
relative permeabilities ranging from 100 to 100,000.
It may be noted from (2.1) that
H 2 p D ¼ i
ð 2 : 4 Þ
This is a particular case of an important general principle of electromagnetism.
The line integral of H around a closed path is equal to the total current enclosed or
magnetomotive force (m.m.f.) F :
þ H d l ¼ F
ð 2 : 5 Þ
¨ ersted's discovery implies that a current exerts a force on a magnet, and in
particular on the magnet's field. It may be inferred from Newton's third law                   Search WWH ::

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