Two long, parallel transmission lines, 41.5 cm apart, carry 27.0-A and 79.0-A cu
ID: 1374256 • Letter: T
Question
Two long, parallel transmission lines, 41.5 cm apart, carry 27.0-A and 79.0-A currents. (a) Find all locations where the net magnetic field of the two wires is zero ?f the currents are in the same direction. B tot = 0 along a line m from the wire carrying 79.0 A and m from the wire carrying current 27.0 A. (b) Find all locations where the net magnetic field of the two wires is zero if the currents are ?n the opposite direction. B tot = 0 along a line m from the wire carrying 27.0 A and m from the wire carrying current 79.0 A.Explanation / Answer
Note that the magnitude of the B field due to a long wire is
B = uo I / [2 pi r]
where r is the distance from the wire.
If they have current in the same direction, then
Bnet = 0 = uo (27.0 A) / [2 pi d] - uo [79.0 A] / [2 pi (0.415 m - d)]
where d = the distance from the 27.0 A wire.
Thus, solving for d,
d = 0.106 m
Thus:
Btot = 0 along a line 0.309 m from the wire carrying 79.0 A and 0.106 m from the wire carrying 27.0 A. [ANSWER, PART A]
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Note that the magnitude of the B field due to a long wire is
B = uo I / [2 pi r]
where r is the distance from the wire.
If they have current in the opposite direction, then
Bnet = 0 = uo (27.0 A) / [2 pi d] - uo [79.0 A] / [2 pi (0.415 m + d)]
where d = the distance from the 27.0 A wire.
Thus, solving for d,
d = 0.2155 m
Thus:
Btot = 0 along a line 0.2155 m from the wire carrying 27.0 A and 0.6305 m from the wire carrying 79.0 A. [ANSWER, PART B]
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