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296
Chapter 29
SET UP:
The loop when it is completely inside the field region is sketched in Figure 29.26b.
EXECUTE:
For
/2
L
xL
−
<<
the loop is completely inside the
field region and
2
.
B
BL
Φ=
Figure 29.26b
But
0 so
0 and
0.
B
d
I
dt
Φ
==
=
E
There is no force
I
F=l B
!
!
!
×
from the magnetic field and the external force
F
necessary to maintain constant velocity is zero.
SET UP:
The loop as it enters the magnetic field region is sketched in Figure 29.26c.
EXECUTE:
For 3 /2
L
−
−
the loop is entering the field region.
Let
x
′
be the length of the loop
that is within the field.
Figure 29.26c
Then
and
.
B
B
d
BLx
Blv
dt
Φ
′
=
The magnitude of the induced emf is
B
d
BLv
dt
Φ
E
and the induced
current is
.
BLv
I
R
R
E
Direction of
I
: Let
A
!
be directed into the plane of the figure. Then
B
Φ
is positive. The
flux is positive and increasing in magnitude, so
B
d
dt
Φ
is positive. Then by Faraday&s law
E
is negative, and with
our choice for direction of
A
!
a negative
E
is counterclockwise. The current induced in the loop is
counterclockwise.
SET UP:
The induced current and magnetic force on the loop are shown in Figure 29.26d, for the situation where
the loop is entering the field.
EXECUTE:
I
I
=
F
lB
!
!
!
×
gives that the
force
I
F
!
exerted on the loop by the
magnetic field is to the left and has
magnitude
22
.
I
BLv
B L v
FI
L
B
L
B
R
R
⎛⎞
=
⎜⎟
⎝⎠
Figure 29.26d
The external force
F
!
needed to move the loop at constant speed is equal in magnitude and opposite in direction to
I
F
!
so is to the right and has this same magnitude.
SET UP:
The loop as it leaves the magnetic field region is sketched in Figure 29.26e.
EXECUTE:
For /2
3 /2
L
<
<
the loop is leaving the field
region. Let
x
′
be the length of
the loop that is outside the field.
Figure 29.26e
Then
(
) and
.
B
B
d
BLL x
BLv
dt
Φ
′
−
=
The magnitude of the induced emf is
B
d
BLv
dt
Φ
E
and the induced
current is
.
BLv
I
R
R
E
Direction of
I
: Again let
A
!
be directed into the plane of the figure. Then
B
Φ
is positive
and decreasing in magnitude, so
B
d
dt
Φ
is negative. Then by Faraday&s law
E
is positive, and with our choice for
direction of
A
!
a positive
E
is clockwise. The current induced in the loop is clockwise.
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View Full DocumentElectromagnetic Induction
297
SET UP:
The induced current and magnetic force on the loop are shown in Figure 29.26f, for the situation where
the loop is leaving the field.
EXECUTE:
I
I
=
F
lB
!
!
!
×
gives that the
force
I
F
!
exerted on the loop by the
magnetic field is to the left and has
magnitude
22
.
I
BLv
B L v
F
ILB
LB
R
R
⎛⎞
==
=
⎜⎟
⎝⎠
Figure 29.26f
The external force
F
!
needed to move the loop at constant speed is equal in magnitude and opposite in direction to
I
F
!
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This note was uploaded on 07/16/2011 for the course PHY 2053 taught by Professor Buchler during the Spring '06 term at University of Florida.
 Spring '06
 Buchler
 Physics

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