1
ASSIGNMENT 2
Question 1
The formula of a capacitor is
x
A
C
ε
=
where A is the area of the plates enclosing the
dielectric
ε
between the separation
x
.
Derive the formula of the force
e
f
acting on the
plates based on electrostatic energy
W
e
. Consider a conservative surface enclosing the
capacitor. The electrical power input is
vi
where
v
is the voltage across the capacitor
C
and
dt
dq
i
=
is the current of the capacitor
v
q
C
=
. The mechanical power output is
dt
dx
f
e
.
The rate of change of the electrostatic energy
W
e
is
dt
dx
f
vi
dt
dW
e
e
−
=
dt
dx
f
dt
dq
v
dt
x
q
dW
e
e
−
=
)
,
(
Follow the stepbystep derivation of magnetic energy and magnetic force in the class
notes to derive a formula of electrostatic energy and electrostatic force.
Question 2
Derive the formula of electrostatic coenergy
)
,
(
1
x
v
W
e
and electrostatic force.
The transformation requires changing the state variable from
q
to
v
using:
d(
vq
)=
v
d
q
+
q
d
v
Question 3
The stator iron is separated form the rotor iron an airgap
g
at mean radius
R
. The stack
length is
L
. It is assumed that the permeability in the iron is
iron
μ
= ∞
. The airgap has a
permeability
0
7
4
10
π
=
(S.I. unites). In practical machines,
g<<R
and
g<<L
. The
B
field
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 Spring '09
 BonTekOoi
 Magnetic Field, AIRGAP, Example1

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