Environmental Engineering Reference
In-Depth Information
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
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