maini (nm7637) – hw11 – Shneidman – (12108)
1
This printout should have 11 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
A plane loop oF wire oF area A is placed in a
region where the magnetic feld is perpendicu
lar to the plane. The magnitude oF B varies in
time according to the expression
B
=
B
0
e

at
.
That is, at
t
= 0 the feld is
B
0
, and For
t >
0,
the feld decreases exponentially in time.
±ind the induced emF,
E
, in the loop as a
Function oF time.
1.
E
=
A B
0
e

at
2.
E
=
a B
0
e

at
3.
E
=
a A B
0
e

at
correct
4.
E
=
a A B
0
5.
E
=
a A B
0
e

2
at
6.
E
=
a B
0
t
Explanation:
Basic Concepts:
±araday’s Law:
E ≡
c
E
·
ds
=
−
d
Φ
B
dt
Solution:
Since B is perpendicular to the
plane oF the loop, the magnetic ²ux through
the loop at time
t >
0 is
Φ
B
=
B A
=
A B
0
e

at
Also, since the coe³cient
AB
0
and the pa
rameter a are constants, and ±araday’s Law
says
E
=
−
d
Φ
B
dt
the induced emF can be calculated the From
Equation above:
E
=
−
d
Φ
B
dt
=
−
A B
0
d
dt
e

=
a A B
0
e

That is, the induced emF decays exponentially
in time.
Note:
The maximum emF occurs at
t
= 0
,
where
E
=
a A B
0
.
B
=
B
0
e

at
B
0
0
0
v
t
The plot oF
E
versus
t
is similar to the
B
versus
t
curve shown in the fgure above.
002
10.0 points
The plane oF a rectangular coil, 4
.
8 cm by
6
.
8 cm, is perpendicular to the direction oF a
uniForm magnetic feld
B
.
IF the coil has 45 turns and a total resistance
oF 11
.
3 Ω, at what rate must the magnitude oF
B
change to induce a current oF 0
.
05 A in the
windings oF the coil?
Correct answer: 3
.
84668 T
/
s.
Explanation:
Given :
x
= 4
.
8 cm = 0
.
048 m
,
y
= 6
.
8 cm = 0
.
068 m
,
N
= 45 turns
,
r
= 11
.
3 Ω
,
and
I
= 0
.
05 A
.
The induced emF is
E
=
I R
=
N
d
Φ
dt
=
N
d
(
B A
)
dt
=
N A
d B
dt
,
so
d B
dt
=
I R
N
(
x y
)
=
(0
.
05 A) (11
.
3 Ω)
45(0
.
048 m) (0
.
068 m)
= 3
.
84668 T
/
s
.
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2
003
10.0 points
A conducting bar moves as shown near a long
wire carrying a constant
I
= 40 A current.
I
a
v
L
A
B
If
a
= 8 mm,
L
= 120 cm, and
v
= 15 m
/
s,
what is the potential diFerence, Δ
V
≡
V
A
−
V
B
?
Correct answer: 18 mV.
Explanation:
Given;
E
=
−
d
Φ
B
dt
=
−
d
dt
(
B ℓ x
)
=
−
B ℓ
dx
dt
=
−
B ℓ v .
±rom Ampere’s law, the strength of the
magnetic ²eld created by the long current
carrying wire at a distance
a
from the wire
is
B
=
μ
0
I
2
π a
.
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 Spring '08
 moro
 Magnetic Field, Lenz

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