127
or so—that breakdown can occur at the insulators that support the
line, whereas in microcircuits and thin-film devices the distances
between components are very small: a 1 volt difference across a
distance of 1 micron gives a field of 1 MV/m.
4.6 MagNetiC Behavior
Magnetic fields are created by moving electric charge—electric
current in electromagnets, electron spin in atoms of magnetic materials. This section is about magnetic materials: how they are characterized and where their properties come from.
Magnetic fields in a vacuum
When a current i passes through a long, empty coil of n turns and
length L, as in Figure 4.56, a magnetic field is generated. The magnitude of the field, H, is given by Ampère’s law as
H
ni
L
=
(4.41)
and thus has units of amps/meter (A/m). The field has both magnitude and direction; it is a vector field.
Magnetic fields exert forces on a wire carrying an electric current.
A current i flowing in a single loop of area S generates a dipole
moment m where
m iS
=
(4.42)
with units A·m
2 , and it too is a vector with a direction normal
to the plane of S (Figure 4.57). If the loop is placed at right
angles to the field H, it feels a torque T (units: Newton·meter, or
N·m) of
T
mH
o
= µ
(4.43)
where µ o is called the permeability of vacuum, µ o = 4πx10
−7 henry/
meter (H/m). To link these we define a second measure of the magnetic field, one that relates directly to the torque it exerts on a unit
magnetic moment. It is called the magnetic induction or flux density,
B, and for vacuum or nonmagnetic materials it is
B
H
o
= µ
(4.44)
Its units are tesla, so a tesla is 1 HA/m
2 . A magnetic induction B of
1 tesla exerts a torque of 1 N·m on a unit dipole at right angles to
the field H.
Figure 4.56
A solenoid creates a magnetic field H; the flux
lines indicate the field strength.
i
i
Flux lines
of field H
2r
n turns
length L
Figure 4.57
Definition of magnetic moment and moment-field
interaction.
Area S
Moment
m
Current i
Torque T
Moment
m
Current i
Field H
Magnetic Behavior
or so—that breakdown can occur at the insulators that support the
line, whereas in microcircuits and thin-film devices the distances
between components are very small: a 1 volt difference across a
distance of 1 micron gives a field of 1 MV/m.
4.6 MagNetiC Behavior
Magnetic fields are created by moving electric charge—electric
current in electromagnets, electron spin in atoms of magnetic materials. This section is about magnetic materials: how they are characterized and where their properties come from.
Magnetic fields in a vacuum
When a current i passes through a long, empty coil of n turns and
length L, as in Figure 4.56, a magnetic field is generated. The magnitude of the field, H, is given by Ampère’s law as
H
ni
L
=
(4.41)
and thus has units of amps/meter (A/m). The field has both magnitude and direction; it is a vector field.
Magnetic fields exert forces on a wire carrying an electric current.
A current i flowing in a single loop of area S generates a dipole
moment m where
m iS
=
(4.42)
with units A·m
2 , and it too is a vector with a direction normal
to the plane of S (Figure 4.57). If the loop is placed at right
angles to the field H, it feels a torque T (units: Newton·meter, or
N·m) of
T
mH
o
= µ
(4.43)
where µ o is called the permeability of vacuum, µ o = 4πx10
−7 henry/
meter (H/m). To link these we define a second measure of the magnetic field, one that relates directly to the torque it exerts on a unit
magnetic moment. It is called the magnetic induction or flux density,
B, and for vacuum or nonmagnetic materials it is
B
H
o
= µ
(4.44)
Its units are tesla, so a tesla is 1 HA/m
2 . A magnetic induction B of
1 tesla exerts a torque of 1 N·m on a unit dipole at right angles to
the field H.
Figure 4.56
A solenoid creates a magnetic field H; the flux
lines indicate the field strength.
i
i
Flux lines
of field H
2r
n turns
length L
Figure 4.57
Definition of magnetic moment and moment-field
interaction.
Area S
Moment
m
Current i
Torque T
Moment
m
Current i
Field H
Magnetic Behavior