Physics 21
Fall, 2004
Solution to HW13
28
P 18
Two long parallel wires 7.0 cm apart carry 16.5 A
currents in the same direction. Determine the magnetic field
strength at a point
P
12.0 cm from one wire and 13.0 cm
from the other.
α
β
α
α
π/2
− α
B
B
1
β
β
π/2
− β
B
2
The field
B
at the point
P
will be the vector sum of the
fields from the two wires. We must find the components of
the two fields so we can add them. We can use the Law of
Cosines to solve for the angles
α
:
13
2
= 12
2
+ 7
2
−
2(12)(7) cos
α
⇒
α
= 81
.
79
◦
12
2
= 13
2
+ 7
2
−
2(13)(7) cos
β
⇒
β
= 66
.
01
◦
The magnitude of the fields are obtained from
B
=
µ
0
I/
2
πR
,
where
R
1
= 0
.
012 m for the left wire and
R
2
= 0
.
013 m for
the right wire. The diagrams show how we can use geometry
to find the components of
B
1
and
B
2
:
B
1
=
µ
0
I
2
π
(0
.
12 m)
−
cos(
π/
2
−
α
)
ˆ
i
+ sin(
π/
2
−
α
)
ˆ
j
B
2
=
µ
0
I
2
π
(0
.
13 m)
−
cos(
π/
2
−
β
)
ˆ
i
−
sin(
π/
2
−
β
)
ˆ
j
Subsituting the numbers, we find
B
=
B
1
+
B
2
= (
−
5
.
04
ˆ
i
−
0
.
64
ˆ
j
)
×
10
−
5
T
28
P 32
A small loop of wire of radius 1.8 cm is placed at
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 Fall '07
 Hickman
 Physics, Current, Magnetic Field, Coaxial cable

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