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Physics 205. Fall 2010. Problem set 4.
1.
Two insulated wires in the xy plane cross at a 30
o
angle but do not make
electrical contact. Each wire carries 5.0 A current (the angle between current
directions is 30
0
). Find magnetic field in two nonequivalent points located 4.0
cm from the intersection, in the xy plane, at equal distances from both wires.
Hint: making a drawing will be very helpful. 24 points
The nonequivalent points 4 cm from the intersection and at equal distances from both
wires in the xy plane are points A and C (did not use B to avoid confusion with the
magnetic field).
For point A I am not even bothering to calculate the shortest distance between this point
and each wire. Using righthand rule one can determine that contributions from both
wires to the field at that point are directed in the opposite ways. Due to symmetry, they
have same amplitudes, and therefore, the total field at point A is ZERO.
For point C, the shortest distance between C and each wire is 4 cm sin75
0
= 3.864 cm.
The field is then (factor 2 is due to two equal contributions from two wires adding up):
T
m
A
A
Tm
a
I
B
5
2
7
0
10
2
.
5
10
864
.
3
14
.
3
5
/
10
14
.
3
4
2
2



⋅
=
⋅
⋅
⋅
⋅
⋅
=
=
π
μ
Units can be just crossed out.
2.
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 Fall '10
 Zazubovits

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