AA320
Background on Electromechanical Energy Conversion (Motors)
.
Conversion of electrical energy to mechanical energy most commonly is carried out by use of
magnetic
fields
.
A magnetic field is characterized by the flux density, B, whose units are Tesla.
[Sometimes B is just
called the magnetic field.].
Bfields can be generated from permanent magnets, or by currents.
Coils of
wire with current flowing in them are commonly used to generate fields.
Note that this is the same
configuration used to make inductors.
[Inductors store
magnetic energy
, whereas capacitors store
electric
field energy
.]
For such a coil, illustrated below, the field inside the coil is B=
μ
NI/
l
, where
μ
is called the
permeability, N is the number of turns, I is the current, and
l
is the length of the coil.
Bfields have a direction in addition to magnitude (they are vectors), and for the coil, the direction of the
field is parallel to the axis of the coil.
The permeability
μ
depends on whether any material is present within
the coil:
μ
=
μ
o
μ
r
where,
μ
o
=4
π
x 10
7
is the freespace value (a constant) and
μ
r
is the relative permeability
(dimensionless) that ranges from 1 for vacuum (or air), to values of several thousand for highly permeable
materials (iron or ferrites).
Use of these high
μ
r
materials allows us to generate high Bfields from relatively
low currents.
Conversion of electrictomechanical energy results from the force that acts on a current that is in a
magnetic field.
The magnitude of the force on a wire of length
l
carrying a current I, in a magnetic field of
strength B is: F= BI
l
sin(
θ
), where
θ
is the angle between the direction of current and the direction of the
magnetic field B.
The direction of this force is given by cross product:
B
x
I
F
r
r
r
=
l
; there is
no
force on a
wire if the magnetic field is parallel to the wire, and the force is maximum if the field direction is
perpendicular
to the wire.
A final consideration is that a
voltage
(sometimes referred to as electromotive force,
emf
) will be developed
in a wire that is exposed to a changing magnetic field, or equivalently in a wire that is
moving
with velocity
u through a fixed magnetic field.
For a single loop of wire in a field that is changing, the voltage
E
is given
by:
E
=AdB/dt, where A is the area enclosed by the loop. The field is assumed to point perpendicular to the
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 Fall '09
 Magnetic Field, electrical energy, 90°, 180°

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