Biomedical Engineering Reference
In-Depth Information
location in the magnetic field. These definitions are shown in Fig. 3.2. When
the diameter of the coil is small, the magnetic field becomes similar to that
of a small magnet.
3.1.5
The Current Dipole
To divide the coil into small current elements, the magnetic field can be
approximated by the contribution of all of the current elements. The magnetic
field d
B
(
r
) generated by a current element is expressed by the following
equation:
)=
μ
4
π
I
d
L
N
×
(
R
−
r
)
|
R
−
r
|
d
B
(
r
,
(3.4)
3
where
I
istheelectriccurrentoftheelement,d
L
is the length of the element,
N
r
is the measurement location in the magnetic field. If we use this idea, the
magnetic field can be expressed by the integration of d
is the direction of the element,
R
is the position of the element, and
B
(
r
) along the coil:
(
r
)=
c
B
d
B
(
r
)d
L.
(3.5)
As you can imagine from this example, a general magnetic source can be
approximated by the summation of current elements with the length being
small. Therefore, such a small current element itself is one of the most funda-
mental magnetic sources. We can rewrite (3.4) as the magnetic field expres-
sion of a small current element:
B
cd
(
r
)=
μ
4
π
i
N
×
(
R
−
r
)
,
(3.6)
3
|
R
−
r
|
where
i
=
I
d
L
. From the physics viewpoint of the current element, the
length of the element is relatively small in comparison with the distance from
R
. In this case, we can regard the element as a point of current flow.
The parameter
i
is called the electric current dipole moment. The concept
of current flow is called the electric current dipole, proposed by Biot and
Savart (the Biot-Savart law). From these considerations, we could reconstruct
the magnetic field of a source magnet by considering the number of electric
current dipoles. This is called the equivalent current dipole model.
to
r
3.1.6
Time-Varying Magnetic Fields
Magnetic fields sometimes vary. This is mostly caused by variation of the
magnetic source parameter. If we are measuring the ambient magnetic field
at a certain point in the street, and an automobile passes by the magnetic
sensor, we can observe the time-varying magnetic field intensity. In this case,
