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Question

P and Q are long straight conductors 'r' distance apart . N is a point in the plane of wires r/4 distance away from P carrying current I . What is the magnitude and direction of current in the wire Q,so that net magnetic field at N is 0

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Solution

Magnetic field produced by conductor P at point N.BP at N = μ0 I 2π r4 = 2μ0 I πrThe magnitude of the magnetic field at N produced by the conductor Q should be exactly equal to BP at N but in opposite direction it negate its effect.Therefore,BQ at N = μ0 I' 2π 3r4 = 23 μ0 I' πror,23 μ0 I' πr = BP at N =2μ0 I πrI' = 3INow, the direction of the current in Q should be opposite ot the direction of the current in Pas per the right hand thumb rule to create the desired effect.

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