Biomedical Engineering Reference
In-Depth Information
F
(N/m) is the force vector per unit length of conductor,
I
(A) is the current vector,
where
B
(weber/m
2
)
and
is the magnetic vector or flux density. The relationship among these
vectors can be determined using the right-hand rule, which states that if the index finger
is pointing in the direction of the current flow and the middle finger is aligned with the
magnetic field, then the thumb, extended perpendicular to the two fingers, points in the
direction of the force.
The magnitude of the force,
F
(N), depends on the total length,
l
(m), of the conductor
in the field, the magnetic flux,
B
(weber/m
2
)
, and the current,
I
(A), if all the components
are orthogonal
F
=
BIl
(3.2)
This equation is extended later in this chapter to determine the force generated by a
solenoid and the torque generated by an electric motor.
A second consideration of importance is the relationship among the magnetic flux,
B
,
produced by a conductor wound into a coil (known as a solenoid), the current,
I
, flowing
through the solenoid, and the number of turns,
N
. If the solenoid is long compared with
its diameter, then the field in its center can be approximated by
B
=
μ
o
NI
L
(3.3)
where
μ
o
=
4
π
×
10
−
7
(weber/amp-m) is the permeability of free space, and
L
(m) is the
length of the solenoid.
The flux density drops off toward the ends of the coil, and within one radius it reduces
to 15% as the flux leaks out. This effect is illustrated in Figure 3-1.
FIGURE 3-1
Flux density along the length of a coil. (a) Cross-section through coil showing
magnetic flux lines. (b) Relationship between the magnetic flux density and the distance from
the centre of the solenoid.
