sanne (as42476) – Homework 09 – Yao – (59110)
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001
10.0 points
The Wb/m
2
is a unit of
1.
force.
2.
magnetic flux.
3.
pressure.
4.
magnetic field.
correct
5.
area.
Explanation:
We know that Wb is the unit of magnetic
flux, so Wb/m
2
is the unit of magnetic field,
in fact 1 Wb/m
2
= 1 T.
002
10.0 points
A flat coil of wire consisting of 33 turns, each
with an area of 20 cm
2
, is positioned perpen
dicularly to a uniform magnetic field that in
creases its magnitude at a constant rate from
2
.
4 T to 8
.
1 T in 1
.
3 s. If the coil has a total
resistance of 0
.
91 Ω, what is the magnitude of
the induced current?
Correct answer: 0
.
318005 A.
Explanation:
E
=
−
d
Φ
B
dt
Φ
B
=
N
integraldisplay
vector
B
·
d
vector
A
=
N B A
E
=
N A
(
B
2
−
B
1
)
t
I
=
E
R
=
N A
(
B
2
−
B
1
)
R t
=
0
.
318005 A
.
keywords:
003
10.0 points
A
twoturn
circular
wire
loop
of
radius
0
.
431 m lies in a plane perpendicular to a
uniform magnetic field of magnitude 0
.
474 T.
Now the wire is reshaped from a twoturn
circle to a oneturn circle in 0
.
0526 s (while
remaining in the same plane).
What is the magnitude of the average in
duced emf in the wire during this time?
Correct answer: 15
.
7768 V.
Explanation:
Basic Concept:
Faraday’s Law is
E
=
−
N
d
Φ
B
dt
.
Let :
r
2
= 0
.
431 m
,
r
1
= 2
r
2
= 2 (0
.
431 m) = 0
.
862 m
,
A
2
=
π r
2
2
= 0
.
583585 m
2
,
A
1
=
π r
2
1
=
π
(2
r
2
)
2
= 2
.
33434 m
2
,
Δ
t
= 0
.
0526 s
,
and
B
= 0
.
474 T
.
The wire has a constant length,
conse
quently the circumference (and radius) of the
one turn loop will be twice the circumfer
ence (and radius) of the two turn loop, since
c
= 2
π r .
When the wire loop’s shape changed, the
radius also changed;
i.e.
,
r
1
= 2
r
2
, where
subscript 1 denote the new oneturn loop.
r
1
is the radius of the new oneturn loop, and
r
2
is the radius of the twoturn loop.
The the change in area
A
=
π r
2
, lead to
the change of the magnetic flux.
ΔΦ
B
= Φ
B
1
−
Φ
B
2
=
π
(2
r
2
)
2
·
B
−
π r
2
2
·
B
= 3
π r
2
2
B
= 3
π
(0
.
431 m)
2
(0
.
474 T)
= 0
.
829858 Wb
.
From Faraday’s law, the average induced emf
in this period is
E
=
vextendsingle
vextendsingle
vextendsingle
vextendsingle
−
d
Φ
B
dt
vextendsingle
vextendsingle
vextendsingle
vextendsingle
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sanne (as42476) – Homework 09 – Yao – (59110)
2
=
vextendsingle
vextendsingle
vextendsingle
vextendsingle
ΔΦ
B
Δ
t
vextendsingle
vextendsingle
vextendsingle
vextendsingle
=
vextendsingle
vextendsingle
vextendsingle
vextendsingle
(0
.
829858 Wb)
(0
.
0526 s)
vextendsingle
vextendsingle
vextendsingle
vextendsingle
= 15
.
7768 V
.
004
10.0 points
A circular conducting loop is held fixed in
a uniform magnetic field that varies in time
according to
B
(
t
) =
B
0
exp(
−
a t
) where
t
is
in s,
a
is in s

1
and B is the field strength
in
T
at
t
= 0. At
t
= 0, the emf induced in
the loop is 0
.
084 V
.
At
t
= 1
.
97 s, the emf is
0
.
0304 V
, .
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 Spring '08
 Turner
 Physics, Force, Work, Magnetic Field, Lenz

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