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236
Faraday’s Law
*P31.68
(a)
εθ
θ
ω
=−
°=−
=
N
d
dt
BA
d
dt
B
a
Ba d
dt
Ba
cos
cos
.
.
..
1
2
0
2
1
2
1
2
05
2
0125
2
2
2
2
T
m
r
a
d
s
V
V clockwise
af
a
f
The – sign indicates that the induced emf produces clockwise current, to make its own
magnetic field into the page.
(b)
At this instant
θω
==
=
t
20
2
5
0
5
rad s
s
rad
. The arc
PQ
has length
r
==
=
025
...
rad
m
m
a
f
. The length of the circuit is 0 5
0 5
0 25
1 25
.
m
m
m
m
++
=
its
resistance is
125
625
m5
m
ΩΩ
bg
=
. The current is
00200
.
.
V
6.25
A clockwise
Ω
=
.
*P31.69
Suppose the field is vertically down. When an electron is moving away
from you the force on it is in the direction given by
q
c
vB
×
as
−×
=
−
away
down
=
left
right .
Therefore, the electrons circulate clockwise.
FIG. P31.69
(a)
As the downward field increases, an emf is induced to produce some current that in turn
produces an upward field. This current is directed
counterclockwise, carried by
negative electrons moving clockwise. Therefore the original electron motion speeds up.
(b)
At the circumference, we have
Fm
a
cc
∑
=
:
qvB
mv
r
c
sin90
2
°=
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Current

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