lim (kl9356) – Homework 16 – Weathers – (22202)
1
This
printout
should
have
14
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
001
10.0 points
The plane of a rectangular coil of dimension
5 cm by 8 cm is perpendicular to the direction
of a magnetic field
B
. The coil has 171 turns
and a total resistance of 10
.
3 Ω.
At what rate must the magnitude of
B
change in order to induce a current of 0
.
0368 A
in the windings of the coil?
Correct answer: 0
.
554152 T
/
s.
Explanation:
Basic Concepts:
Faraday’s Law of Induc
tion
E
=
−
d
Φ
B
dt
Ohm’s law
I
=
V
R
Solution:
With Ohm’s law, the emf induced
in one turn of coil is
E
1
=
I R
n
=
(0
.
0368 A) (10
.
3 Ω)
(171 turns)
= 0
.
00221661 V
,
while with Faraday’s law, we get
E
1
=
d
Φ
B
dt
=
d
(
A
·
B
)
dt
=
A
d B
dt
.
So, the rate at which magnetic field changes
will be
d B
dt
=
E
1
A
=
(0
.
00221661 V)
(0
.
004 m
2
)
= 0
.
554152 T
/
s
.
002
(part 1 of 2) 10.0 points
The counterclockwise circulating current in
a solenoid is increasing at a rate of 9
.
44 A
/
s.
The crosssectional area of the solenoid is
3
.
14159 cm
2
, and there are 330 turns on its
12
.
2 cm length.
What is the magnitude of the induced
E
produced by the increasing current?
Correct answer: 3
.
32659 mV.
Explanation:
Faraday’s Law for solenoid:
E
=
−
N
d
Φ
dt
=
−
N A
d B
dt
.
Magnetic field produced by the changing
current is
B
=
μ
0
N I
L
d B
d t
=
μ
0
N
L
d I
d t
.
Faraday’s Law for solenoid:
E
=
−
N
d
Φ
dt
=
−
N
d
(
BA
)
dt
=
−
N
2
A
L
μ
0
d I
d t
.
Magnetic field induced by current:
B
=
μ
0
N I
L
.
Thus, the induced
E
is
E
=
μ
0
N
2
L
A
d I
dt
=
(1
.
25664
×
10

6
N
/
A
2
) (330)
2
12
.
2 cm
×
(3
.
14159 cm
2
) (9
.
44 A
/
s)
×
parenleftbigg
10
3
mV
V
parenrightbigg parenleftbigg
1
10

2
m
cm
parenrightbigg
=
3
.
32659 mV
.
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lim (kl9356) – Homework 16 – Weathers – (22202)
2
003
(part 2 of 2) 10.0 points
Choose the correct statement
1.
The
E
attempts to move the current in the
solenoid in the clockwise direction
correct
2.
Not enough information is given to deter
mine the effect of the
E
3.
The
E
does not effect the current in the
solenoid
4.
By the right hand rule, the
E
produces
magnetic fields in a direction perpendicular
to the prevailing magnetic field
5.
The
E
tries to keep the current in the
solenoid flowing in the counterclockwise di
rection
Explanation:
As the current is increasing in the counter
clockwise direction, by Lenz’s law, the
E
will
attempt to retard the current, which estab
lishes an
E
that tries to counter the flow of
the current, which in this case would be in the
clockwise direction.
004
10.0 points
An 18
.
6 turns circular coil with radius 9
.
56 cm
and resistance 6
.
87 Ω is placed in a magnetic
field directed perpendicular to the plane of
the coil. The magnitude of the magnetic field
varies in time according to the expression
B
=
a
1
t
+
a
2
t
2
,
where
a
1
= 0
.
0934 T
/
s,
a
2
= 0
.
0962 T
/
s
2
are
constants, time
t
is in seconds and field
B
is
in Tesla.
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 Spring '00
 Littler
 Magnetism, Work, Magnetic Field, lim

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