F
B
,
i
5
BA
cos
0°
5
1
6.0
3
10
2
5
T
21
12
3
10
2
4
m
2
21
1
2
5
7.2
3
10
2
8
Wb.
F
B
f
f
5
90°.
f
i
5
0°.
F
B
5
BA
cos
f
.
E
5
P
DF
B
D
t
P
.
P
D
B
D
t
P
5
RI
NA
5
1
40.0
V
21
0.150 A
2
1
200
2
p
1
3.00
3
10
2
2
m
2
2
5
10.6 T
/
s.
I
5
E
R
5
NA
0
D
B
/
D
t
0
R
.
E
5
N
P
DF
B
D
t
P
5
NA
P
D
B
D
t
P
.
f 5
0°,
F
B
5
BA
cos
f
.
E
5
N
P
DF
B
D
t
P
.
I
5
E
R
5
0.0171 V
0.600
V
5
0.0285 A.
E
5
A
D
B
D
t
5
1
0.0900 m
2
21
0.190 T
/
s
2
5
0.0171 V.
f 5
0°,
F
B
5
BA
cos
f
.
E
5
P
DF
B
D
t
P
.
D
2
5
D
/
"
2
.
D
1
5
D
.
D
2
2
5
1
2
D
1
2
,
A
5
1
2
p
D
2
A
2
5
A
1
/
2.
F
B
5
BA
cos
f
.
212
Chapter 21
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21.10.
Set Up:
At
let the plane of the coil be perpendicular to the magnetic field, so
at
Then
where
is the angular velocity of the coil. B Since the field is uniform,
A
sketch of
is given in Figure 21.10a.
Figure 21.10
Solve: (a)
The instantaneous value of the induced emf equals the rate of change of the flux and this is
the slope of the curve in Figure 21.10a. From point
A
to point
B
this slope is negative and increasing in magnitude
and from
B
to
C
it is negative and decreasing in magnitude. From point
C
to
D
this slope is positive and increasing
and from
D
to
E
it is positive and decreasing. After point
E
the behavior of
repeats. Therefore, the induced emf
increases and decreases periodically and reverses sign.
(b)
The induced emf versus time is sketched in Figure 21.10b.
21.11.
Set Up:
The maximum emf is produced when the opposite sides of the coil are moving perpendicular to the
field with speed
The maximum emf induced in each of the two sides on one turn is
The maximum
total emf is
Solve: (a)
(b)
The emf changes polarity as the coil rotates and the average emf is zero.
Reflect:
The maximum emf is proportional to the angular velocity of the coil. As
increases, the flux through the
coil changes more rapidly.
21.12.
Set Up:
The field of the induced current is directed to oppose the change in flux in the primary circuit.
Solve: (a)
The magnetic field in
A
is to the left and is increasing. The flux is increasing so the field due to the
induced current in
B
is to the right. To produce magnetic field to the right, the induced current flows through
R
from
right to left.
(b)
The magnetic field in
A
is to the right and is decreasing. The flux is decreasing so the field due to the induced cur
rent in
B
is to the right. To produce magnetic field to the right the induced current flows through
R
from right to left.
(c)
The magnetic field in
A
is to the right and is increasing. The flux is increasing so the field due to the induced cur
rent in
B
is to the left. To produce magnetic field to the left the induced current flows through
R
from left to right.
(d)
The magnetic field of
A
is constant so the flux through
B
is constant and there is no induced emf and no induced
current.
21.13.
Set Up:
The field of the induced current is directed to oppose the change in flux.
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 Spring '09
 RODRIGUEZ
 Physics, Flux, Magnetic Field

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