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yang (ey942) – 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 (part 1 of 2) 10.0 points
Consider two long parallel wires which are
perpendicular to the plane oF the paper (
i.e.
,
the
x

y
plane). Both wires carry the same
current,
I
.
Wire #1 intersects the plane a distance
a
above point
O
and wire #2 intersects the
plane a distance
a
below point
O
.
Point
C
is equidistant From both wires and
is a distance
a
From point
O
.
a
a
a
a
O
C
D
wire #2
wire #1
45
◦
45
◦
x
y
I
II
III
IV
O
What is the direction oF the magnetic feld
at
C
?
1.
in the negative
y
direction
2.
in quadrant III
3.
into the plane
4.
in the positive
x
direction
5.
in quadrant IV
6.
in quadrant II
7.
in the negative
x
direction
8.
in the positive
y
direction
correct
9.
out oF the plane
10.
in quadrant I
Explanation:
B
2
B
1
O
C
wire #2
wire #1
±rom this fgure, we can see by symmetry
that the
y
components oF the magnetic felds
cancel, leaving only the component in the
positive
x
direction.
002 (part 2 of 2) 10.0 points
What is the magnitude oF the magnetic feld
at
C
?
1.
B
C
=
1
2
μ
0
I
a
2.
B
C
=
1
4
π
μ
0
I
a
3.
B
C
=
1
√
2
π
μ
0
I
a
4.
B
C
=
1
2
√
2
μ
0
I
a
5.
B
C
=
1
4
μ
0
I
a
6.
B
C
=
1
√
2
μ
0
I
a
7.
B
C
= 0
8.
B
C
=
1
2
√
2
π
μ
0
I
a
9.
B
C
=
1
π
μ
0
I
a
10.
B
C
=
1
2
π
μ
0
I
a
correct
Explanation:
Note:
The distance
r
From each wire to
C
is
r
=
a
sin 45
◦
=
√
2
a .
The magnitude oF the
x
component oF the
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View Full Documentyang (ey942) – ohw19 – turner – (56705)
2
magnetic feld due to each wire at
C
is given
by
B
1
=
B
2
=
μ
0
I
2
π
√
2
a
cos 45
◦
=
μ
0
I
2
π
√
2
a
1
√
2
=
μ
0
I
4
π a
.
Hence the contribution From both wires at
C
is just twice this value:
B
C
= 2
B
1
=
μ
0
I
2
π a
.
003
10.0 points
A circular loop oF wire oF radius
R
= 4
.
2 m
lies in the
xy
plane, centered about the origin.
The loop is carrying a current oF
I
= 5
.
88 A
±owing in counterclockwise direction.
Consider two
l
= 1
.
73 mm segments oF the
loop: one centered about the positive
x
axis,
the other centered about the positive
y
axis.
Hint:
Use BiotSavart law.
The
permeability
oF
Free
space
is
1
.
25664
×
10
−
6
Tm
/
A
.
R
y
x
I
r
l
=ds
1
I
2
1
1
l
=ds
2
2
What is the magnitude oF the Force the frst
exerts on the second?
Correct answer: 2
.
07397
×
10
−
13
N.
Explanation:
Let :
μ
0
= 1
.
25664
×
10
−
6
Tm
/
A
,
l
= 1
.
73 mm = 0
.
00173 m
,
I
= 5
.
88 A
,
and
R
= 4
.
2 m
.
Since the radius,
R
, oF the current loop is
much bigger than the length,
l
, oF both small
segments, we can regard the segments as a
small straight line.
²rom the BiotSavart law
d
v
B
=
μ
0
I
4
π
dvs
×
ˆ
r
r
2
.
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 Spring '10
 Turner

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