Two long parallel transmission lines 38.0 cm apart carry 27.5 A and 78.0 A curre

Question

Two long parallel transmission lines 38.0 cm apart carry 27.5 A and 78.0 A currents. Find all locations where the net magnetic field of the two wires is zero if these currents are in the same direction. Please, enter your answer as a distance from the wire carrying 27.5 A. Find all locations where the net magnetic field of the two wires is zero if these currents are in opposite directions. Please, enter your answer as two distances, the first distance from the wire carrying 27.5 A, and the second distance from the wire carrying 78.0 A. Separate the values with a comma.

Explanation / Answer

Expression for the magnetic field due to straight current carrying conductor at a distance "d" as K*I/d
If current are in the same direction then the null point has to lie within the two conductors.
Let x be the distance of the point from 25A conductor. Then the point is at 0.38-x right from 78A conductor
So as they have to be equal in magnitude, we get 25/x = 78/(0.38-x)
Or 9.5-25x = 78x
Or x = 0.09m
So the point will be at a distance 0.09m right from 25A conductor

Part b)
Now if current flows in opposite direction then null points could be outside on both sides.'
Say it is at x1 right from 25A conductor side.
So 25/x1 = 78/(0.38+x1)

78x1=9.5+25x1
OR x1 = 0.179m. This means it is at 0.55m right from 78A conductor
If it is on 78A side then 25/(0.38+x2) = 78/x2

25x2=29.64+78x2
OR x2 = - 0.55m
So it is not valid. Hence there will be only one point outside and that too nearby 25A conductor
Hence two points:
1. At a distance 0.09m in between right from 25A conductor
2. At a distance 0.179m outside right from 25A conductor

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