Rodriguez, Brandon – Homework 13 – Due: Oct 5 2006, 11:00 am – Inst: Andrew J Rader
1
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before answering.
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time, but before the DUE DATE on top of
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REMEMBER
THAT
YOU
MUST CARRY OUT YOUR CALCULA
TIONS TO AT LEAST THREE SIGNIFI
CANT FIGURES. YOUR ANSWER MUST
BE
WITHIN
ONE
PERCENT
OF
THE
CORRECT RESULT TO BE MARKED AS
CORRECT BY THE SERVER.
001
(part 1 of 1) 8 points
The segment of wire in the figure carries a
current of 8 A, where the radius of the circular
arc is 5 cm.
The
permeability
of
free
space
is
1
.
25664
×
10

6
T
·
m
/
A
.
8 A
5 cm
O
Determine the magnitude of the magnetic
field at point
O ,
the origin of the arc.
Correct answer: 25
.
1327
μ
T.
Explanation:
Let :
I
= 8 A
and
R
= 5 cm = 0
.
05 m
.
For the straight sections d
~s
×
ˆ
r
= 0.
The
quarter circle makes onefourth the field of a
full loop
B
=
μ
0
I
8
R
into the paper.
Or, you
can use the equation
B
=
μ
o
I
4
π
θ ,
where
θ
=
π
2
.
Thus the magnetic field is
B
=
μ
0
I
8
R
,
=
(1
.
25664
×
10

6
T
·
m
/
A) (8 A)
8 (0
.
05 m)
=
25
.
1327
μ
T
,
into the paper
.
keywords:
002
(part 1 of 1) 8 points
A long, thin conductor carries a current of
13
.
8 A.
At what distance from the conductor is
the magnitude of the resulting magnetic field
9
.
62
×
10

5
T?
Correct answer: 2
.
86902 cm.
Explanation:
Let :
μ
0
= 1
.
25664
×
10

6
N
/
A
2
,
B
= 9
.
62
×
10

5
T
,
and
I
= 13
.
8 A
.
By the BiotSavart Law,
B
=
μ
0
I
2
π r
r
=
μ
0
I
2
π B
=
(1
.
25664
×
10

6
N
/
A
2
) (13
.
8 A)
2
π
(9
.
62
×
10

5
T)
= 0
.
0286902 m
=
2
.
86902 cm
.
keywords:
003
(part 1 of 2) 8 points
A conductor in the shape of a square, whose
sides are of length 0
.
76 m, carries a clockwise
13 A current as shown in the figure below.
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Rodriguez, Brandon – Homework 13 – Due: Oct 5 2006, 11:00 am – Inst: Andrew J Rader
2
0
.
76 m
13 A
P
What is the magnitude of the magnetic field
at point
P
(at the center of the square loop)
due to the current in the wire?
Correct answer: 19
.
3524
μ
T.
Explanation:
Let :
μ
0
= 1
.
25664
×
10

6
T m
/
A
,
‘
= 0
.
76 m
and
I
= 13 A
.
By the BiotSavart law,
dB
=
μ
0
4
π
I d~s
×
ˆ
r
r
2
.
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 Spring '08
 pedon
 Work, Magnetic Field, Andrew J Rader

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