song (shs546) – Homework 14 – weathers – (22202)
1
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printout
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have
15
questions.
Multiplechoice questions may continue on
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before answering.
001(part1of4)10.0points
Four long, parallel conductors carry equal cur
rents.
A crosssectional view of the conduc
tors is shown in the figure.
Each side of the
square has length of 0
.
9 m. The current direc
tion is out of the page at points indicated by
the dots and into the page at points indicated
by the crosses.
A
B
C
D
×
×
×
P
x
y
0
.
9 m
2 A
2 A
2 A
2 A
Which diagram correctly denotes the di
rections
of
the
components
of
the
mag
netic field from each conductor at the point
P
?
The
permeability
of
free
space
is
1
.
25664
×
10
−
6
N
/
A
2
.
1.
P
B
A
B
B
B
C
B
D
2.
P
B
A
B
B
B
C
B
D
3.
P
B
A
B
B
B
C
B
D
correct
4.
P
B
A
B
B
B
C
B
D
5.
P
B
A
B
B
B
C
B
D
6.
P
B
A
B
B
B
C
B
D
Explanation:
Let :
I
= 2 A
and
ℓ
= 0
.
9 m
.
The directions of the magnetic field due
to each wire are given by the right hand rule,
where the thumb points in the direction of the
current and your fingers curl in the direction
of the magnetic field’s circular path.
Consider the magnetic field contributions
due to the currents in
A
and
B
only:
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song (shs546) – Homework 14 – weathers – (22202)
2
A
B
×
P
2 A in
2 A out
B
A
B
B
Consider the magnetic field contributions
due to the currents in
C
and
D
only:
C
D
×
×
P
2 A in
2 A in
B
C
B
D
Consider the results of all four magnetic
field contributions superimposed on one an
other:
A
B
C
D
×
×
×
P
0
.
9 m
2 A in
2 A out
2 A in
2 A in
B
A
B
B
B
C
B
D
002(part2of4)10.0points
What is the magnitude of each of the four
components
B
A
,
B
B
,
B
C
, and
B
D
at the
point P?
1.
bardbl
vector
B
A,B,C,
or
D
bardbl
=
μ
0
I
2
2
π ℓ
2.
bardbl
vector
B
A,B,C,
or
D
bardbl
=
μ
0
I
2
π ℓ
3.
bardbl
vector
B
A,B,C,
or
D
bardbl
=
μ
0
I
√
2
π ℓ
correct
4.
bardbl
vector
B
A,B,C,
or
D
bardbl
=
μ
0
I ℓ
2
π
5.
bardbl
vector
B
A,B,C,
or
D
bardbl
=
μ
0
I
2
√
2
π ℓ
Explanation:
By Ampere’s law, the line integral around
any closed path is equal to
μ
0
I
.
Here the
path is defined by the circle with radius
r
.
contintegraldisplay
vector
B
·
dvectors
=
μ
0
I
B
·
2
π r
=
μ
0
I
B
=
μ
0
I
2
π r
,
where
r
=
ℓ
cos 45
◦
=
ℓ
√
2
is the distance from
any of the wires to P, from which it follows
that
B
A
=
B
B
=
B
C
=
B
D
.
B
A
=
μ
0
I
√
2
π ℓ
.
003(part3of4)10.0points
What is the magnitude of the magnetic field
at point
P
?
1.
vextenddouble
vextenddouble
vextenddouble
vector
B
net
vextenddouble
vextenddouble
vextenddouble
= (1
.
41421)
vextenddouble
vextenddouble
vextenddouble
vector
B
A,B,C, or D
vextenddouble
vextenddouble
vextenddouble
2.
vextenddouble
vextenddouble
vextenddouble
vector
B
net
vextenddouble
vextenddouble
vextenddouble
= 0
vextenddouble
vextenddouble
vextenddouble
vector
B
A,B,C, or D
vextenddouble
vextenddouble
vextenddouble
3.
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 Spring '00
 Littler
 Work, Magnetic Field, Bnet, Bnet Bnet Bnet

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