Biomedical Engineering Reference
In-Depth Information
10
4
Webers/m
2
), m
0
¼
10
7
where the magnetic flux
B
is in units of Webers (1 Tesla(T)
¼
4
p
Henry/m [Weber/(amp-meter)] is the permeability of free space,
is current in Amperes,
I
and
is the radial distance from the wire in meters. The right-hand rule applies: As the fin-
gers curl about the direction of the
r
B
field, the thumb points in the direction of the current.
EXAMPLE PROBLEM 16.10
Calculate the magnetic field in
T
at 5 mm from a wire carrying 20 A of current.
Solution
Using Eq. (16.48),
4
p
e
7
20
m
2
10
4
m
2
10
6
T
B
f
¼
ð
Weber
=
Þ
1T
=
ð
Weber
=
Þ¼
8
2
p
5
e
3
If the wire is coiled into a circular loop, a magnetic dipole with north and south poles is
created. As a second case, an equivalent situation is created by a rotating charge, as shown
in Figure 16.28. Current
I
, flowing along an increment of wire
dl
, in a loop is equivalent to a
charge
. The magnetic dipole moment is the product
of the equivalent current and area at a large distance
q
, of mass
m
, orbiting at a frequency,
v
r
,
1
2
qr
2
2
m ¼ð
qvA
Þ
z
¼
qvpr
z
¼
o
z
ð
16
:
49
Þ
m
z
where the direction of
according to the right-hand rule. A vector is a
quantity that has a magnitude and a direction; in this case, a unit vector has a magnitude of
one and is directed along the
is along unit vector
z
-axis. If the mass of the charge is
m
, the orbital angular
momentum is
2
L
¼
mr
o
ð
16
:
50a
Þ
The classic gyromagnetic ratio is defined as
g
c
¼
m
L
¼
2
ð
16
:
50b
Þ
m
z
m
y
I
r
v
q
x
F
FIGURE 16.28
Magnetic dipole moment of a charge in a circular orbit.
