PHY2061
R. D. Field
Solutions
Chapter 34
Page 1 of 6
Chapter 34 Solutions
Problem 1:
A long straight wire carries current
I
.
Nearby
and lying in the same plane is a circular loop, as
shown in the
Figure
.
If the loop is moved
toward the wire, what will be the direction of the
current induced in the loop (if any) and what
will be the direction of any electromagnetic
force exerted on the loop?
Answer:
counterclockwise; away from the wire
Solution:
Pushing the wire loop toward the current carrying wire causes
the magnetic flux to increase in the loop and thus the induced current will
flow in a
counterclockwise direction
so that the induced magnetic field
will be up
(opposite to the increasing downward external magnetic field).
The force on the loop is in a direction that opposes the push (i.e.
away from
the straight wire
).
Problem 2:
A magnetic field given by
B(t) = at+b
with
a = 1 T/s
and
b = 1 T
is
directed perpendicular to the plane of a circular coil of
10 turns
and radius
0.2 m
.
If the coil’s total resistance is
1.58 Ohms
, how much power (
in
Watts
) is dissipated at time
t = 1 s
?
Answer:
1
Solution:
The magnetic flux through the loop is
Φ
B
= NB
Α
and from
Faraday’s Law
we have,
NAa
dt
dB
NA
dt
d
B
−
=
−
=
Φ
−
=
ε
.
At
t = 1 second
(actually at any time t) this gives
R
NAa
R
I
=
=
ε
,
and power
W
s
T
R
a
A
N
R
I
P
1
58
.
1
)
/
1
(
)
2
.
0
(
)
100
(
2
4
2
2
2
2
2
=
Ω
=
=
=
π
.
I
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PHY2061
R. D. Field
Solutions
Chapter 34
Page 2 of 6
Problem 3:
A
25turn
coil of resistance
3 Ohms
has area of
8 cm
2
. Its plane is
perpendicular to a magnetic field given by
B(t) = 0.4t  0.3t
2
(where B is in
Tesla and t is in seconds).
What is the induced current in the coil (
in
milliA
) at
t = 1 second
?
Answer:
1.33
Solution:
The magnetic flux through the loop is
Φ
B
= NB
Α
and from
Faraday’s Law
we have,
)
6
.
0
4
.
0
(
t
NA
dt
dB
NA
dt
d
B
−
−
=
−
=
Φ
−
=
ε
.
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 Spring '08
 FRY
 Physics, Current, Magnetic Field, Faraday, loop

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