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Physics 21
Fall, 2004
Solution to HW13
28
P18
Two long parallel wires 7.0 cm apart carry 16.5 A
currents in the same direction. Determine the magnetic feld
strength at a point
P
12.0 cm From one wire and 13.0 cm
From the other.
αβ
α
α
π/2
− α
B
B
1
β
β
π/2
− β
B
2
The feld
B
at the point
P
will be the vector sum oF the
felds From the two wires. We must fnd the components oF
the two felds 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
2
−
2(13)(7) cos
β
⇒
β
=66
.
01
◦
The magnitude oF the felds are obtained From
B
=
µ
0
I/
2
πR
,
where
R
1
=0
.
012 m For the leFt wire and
R
2
.
013 m For
the right wire. The diagrams show how we can use geometry
to fnd the components oF
B
1
and
B
2
:
B
1
=
µ
0
I
2
π
(0
.
12 m)
³
−
cos(
π/
2
−
α
)
ˆ
i
+sin(
2
−
α
)
ˆ
j
´
B
2
=
µ
0
I
2
π
(0
.
13 m)
³
−
cos(
2
−
β
)
ˆ
i
−
sin(
2
−
β
)
ˆ
j
´
Subsituting the numbers, we fnd
B
=
B
1
+
B
2
=(
−
5
.
04
ˆ
i
−
0
.
64
ˆ
j
)
×
10
−
5
T
28
P32
A small loop oF wire oF radius 1.8 cm is placed at
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This note was uploaded on 08/06/2008 for the course PHYS 21 taught by Professor Hickman during the Fall '07 term at Lehigh University .
 Fall '07
 Hickman
 Physics, Current

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