nguyen (jmn727) – homework 29 – Turner – (59070)
1
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printout
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have
10
questions.
Multiplechoice questions may continue on
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before answering.
001
10.0 points
What current is required in the windings
of a long solenoid that has 2750 turns uni
formly distributed over a length of 0
.
312 m
in
order
to
produce
a
magnetic
field
of
magnitude 0
.
000113 T at the center of the
solenoid?
The permeability of free space is
4
π
×
10
−
7
T
·
m
/
A
.
Correct answer: 10
.
2021 mA.
Explanation:
Let :
N
= 2750
,
L
= 0
.
312 m
,
B
= 0
.
000113 T
,
and
μ
0
= 4
π
×
10
−
7
T
·
m
/
A
.
The magnetic field inside a long solenoid is
B
=
μ
0
n I
=
μ
0
parenleftbigg
N
L
parenrightbigg
I .
Thus the required current is
I
=
B L
μ
0
N
=
(0
.
000113 T) (0
.
312 m)
(4
π
×
10
−
7
T
·
m
/
A) (2750)
×
1000 mA
1 A
=
10
.
2021 mA
.
002
10.0 points
A single piece of wire is bent into the shape
of Texas, with a total area of 5
.
42 cm
2
. This
Texas shaped loop is perpendicular to a mag
netic field which increases uniformly in mag
nitude from 0
.
812 T to 1
.
65 T in a time of 2 s.
The wire has a total resistance of 3 Ω.
What is the current?
Correct answer: 0
.
0756993 mA.
Explanation:
Basic Concepts:
Faraday’s Law of Induc
tion:
E
=

d
Φ
B
dt
The particular shape of the wire is unimpor
tant, only the area enclosed by the wire mat
ters.
The magnetic flux through the loop is
given by Φ =
B A
.
d
Φ
dt
=
d
dt
(
B A
) =
A
d B
dt
=
A
Δ
B
Δ
t
=
A
B
2

B
1
Δ
t
= (0
.
000542 m
2
)(0
.
419 T
/
s)
= 0
.
000227098 V
.
From Faraday’s Law:
E
=

d
Φ
dt
=

0
.
000227098 V
From Ohm’s Law:
I
=
E
R
=
0
.
000227098 V
3 Ω
= 0
.
0756993 mA
003
10.0 points
A toroid having a rectangular cross section
(
a
= 1
.
11 cm by
b
= 4
.
06 cm) and inner
radius 4
.
95 cm consists of
N
= 440 turns of
wire that carries a current
I
=
I
0
sin
ω t
, with
I
0
= 42 A and a frequency
f
= 69
.
9 Hz.
A
loop that consists of
N
ℓ
= 31 turns of wire
links the toroid, as in the figure.
b
a
N
R
N
l
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nguyen (jmn727) – homework 29 – Turner – (59070)
2
Determine the maximum
E
induced in the
loop by the changing current
I
.
Correct answer: 0
.
334551 V.
Explanation:
Basic Concept:
Faraday’s Law
E
=

d
Φ
B
dt
.
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 Spring '08
 Turner
 Current, Work, Magnetic Field

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