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howard (cah3459) – ohw19 – turner – (56705)
1
This printout should have 18 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
A wire carries a current oF
I
= 44 A along the
x
axis From
x
1
=

5 cm to
x
2
=1
.
6 cm.
I
x
x
P
y
1
x
2
±ind the magnitude oF the resulting mag
netic feld at the point
r
= 4 cm on the
y
axis.
Correct answer: 126
.
785
μ
T.
Explanation:
Let :
x
1
=

5 cm
,
x
2
.
6 cm
,
and
r
= 4 cm = 0
.
04 m
.
±rom the BiotSavart Law
d
&
B
=
μ
0
4
π
I d&s
×
ˆ
r
r
2
,
the magnetic feld at a point From a straight
line segment is
B
=
μ
0
I
4
π r
(cos
θ
1

cos
θ
2
)
.
In this case,
θ
1
= arctan
±
y

x
1
²
= arctan
³
4 cm

(

5 cm)
´
= 38
.
6598
◦
,
and
θ
2
= 180
◦

arctan
±
y
x
2
²
= 180
◦

arctan
±
4 cm
1
.
6 cm
²
= 111
.
801
◦
,
so the resultant magnetic feld is
B
=
μ
0
I
4
π d
(cos
θ
1

cos
θ
2
)
=
μ
0
(44 A)
4
π
(0
.
04 m)
(cos 38
.
6598
◦

cos 111
.
801
◦
)
=
126
.
785
μ
T
.
002 (part 1 of 2) 10.0 points
Imagine a very long, uniForm wire that has a
linear mass density oF 0
.
0033 kg
/
m and that
encircles the Earth at its equator.
Assume the Earth’s magnetic dipole mo
ment is aligned with the Earth’s rotational
axis. The Earth’s magnetic feld is cylindri
cally symmetric (like an ideal bar magnetic).
The acceleration oF gravity is 9
.
8m
/
s
2
and
the magnetic feld oF the earth is 9
×
10

5
T
.
What is the magnitude oF the current in
the wire that keeps it levitated just above the
ground?
Correct answer: 359
.
333 A.
Explanation:
Let :
g
=9
.
/
s
2
,
B
Earth
×
10

5
T
,
and
μ
=0
.
0033 kg
/
m
.
The Earth’s geographical North pole is a mag
netic South pole and
vice versa
. The North
pole oF a compass is attracted to the South
magnetic pole oF the Earth, the place where
Santa Claus lives.
The magnetic and gravitational Forces must
balance. ThereFore, it is necessary to have (For
unit length oF wire)
F
=
IB
=
μg
I
=
B
=
(0
.
0033 kg
/
m) (9
.
/
s
2
)
9
×
10

5
T
=
359
.
333 A
.
howard (cah3459) – ohw19 – turner – (56705)
2
003 (part 2 of 2) 10.0 points
The current in the wire goes in the
1.
same direction as the Earth’s spinning
motion (West to East).
correct
2.
opposite direction as the Earth’s spinning
motion (East to West).
Explanation:
Since the Sun rises in the East, the Earth
is turning towards the East and the Earth’s
angular velocity is parallel to the Earth’s axis,
pointing from South to North.
S
N
v
E
F
B
I
v
Earth
The total force on the wire is zero and
the gravitational force is downward (inward),
so the magnetic force must be upward (out
ward).
If the current goes from West to East, in
the same direction as the Earth’s spinning
motion,
&
I
×
&
B
will be vertically upward (out
ward).
004 (part 1 of 2) 10.0 points
A long, solid cylindrical conductor of radius
0
.
8 m carries a current of 2
.
4 nA parallel to its
axis and uniformly distributed over its cross
section. The conductor has a resistivity of
0
.
006 Ω
·
m.
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