EE Pro for TI-89, 92 Plus
Equations - Motors and Generators
126
31.1 Energy Conversion
The four equations in this section describe the fundamental relationship amongst electrical, magnetic and mechanical
aspects of a system. For example, the first two equations show two ways of computing energy density Wf stored in
a magnetic field. The first equation uses the field intensity H and flux density B in a magnetic region with length L
and area A. The second an electric analogy to the magnetic circuit as it uses the magnetic reluctance Rel and flux
φ
to compute Wf.
Wf
H B L A
= ⋅ ⋅ ⋅ ⋅
1
2
Eq. 31.1.1
Wf
l
= ⋅
⋅
1
2
2
Re
φ
Eq. 31.1.2
The third equation defines the mechanical pressure F due to the flux density B.
F
B
=
⋅
2
2
0
µ
Eq. 31.1.3
The last equation shows the r.m.s. value of the emf Es induced by Ns turns moving with an angular velocity
ω
s
sweeping a magnetic flux of
φ
.
Es
Ns
s
=
⋅ ⋅
ω φ
2
Eq. 31.1.4
Example 31.1 -
A conductor having a length of 15 cm and a cross sectional area of 0.5 cm
2
is subjected to a
magnetic induction of 1.8 T and a field intensity of 2.8 A/m. The magnetic reluctance is 0.46 A/Wb. The conductor
has 32 turns and is moving at a rotational speed of 62 rad/s. Find the magnetic flux, the magnetic energy, the
induced electric field and the mechanical pressure on the coil.
1st Solution: Upper Half
1st Solution: Lower Half
2nd Solution: Upper Half
2nd Solution: Lower Half
Solution -
All of the equations are needed to solve this problem. Press
„
to display the input screen,
enter all the known variables and press
„
to compute the solution. Since the flux is a squared term in the
second equation, there are two equal and opposite results calculated for
φ
and Es.
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