Parallel conductors 

Asked by alanpeter9611 | 14th Feb, 2019, 05:21: PM

Expert Answer:


Cartesian coordinate system is shown in figure to represent the direction of magnetic field at a given point.
 
Magnetic field at A is due to current flow in conductor-2 and coductor 3.
 
In conductor-2 , current flow in -ve y direction.
If we apply right hand rule, we get magnetic fieldat A due to flow of current 3I in conductor 2 = begin mathsize 12px style negative space fraction numerator mu subscript 0 open parentheses 3 I close parentheses over denominator 2 πr end fraction space x with hat on top end style.....................(1)
we get magnetic fieldat A due to flow of current 4I in conductor 3 = begin mathsize 12px style space fraction numerator mu subscript 0 open parentheses 4 I close parentheses over denominator 2 pi open parentheses 3 r close parentheses end fraction space x with hat on top end style........................(2)
By adding eqn.(1) and eqn.(2), we get net magnetic field at A = begin mathsize 12px style open parentheses negative 5 over 3 close parentheses fraction numerator mu subscript o I over denominator 2 πr end fraction space x with hat on top end style
magnetic force on conductor-2 = B×i×L ,   where B is magnetic field on conductor-2, i is the current flowing in conductor-2
and L is the length of conductor-2
 
magnetic force = B×i×L = begin mathsize 12px style open square brackets fraction numerator mu subscript o I over denominator 2 πr end fraction plus fraction numerator mu subscript o 4 I over denominator 2 straight pi open parentheses 2 straight r close parentheses end fraction close square brackets cross times 3 I cross times L space space equals space 9 space fraction numerator mu subscript o I squared over denominator 2 πr end fraction cross times L space N e w t o n end style

Answered by Thiyagarajan K | 14th Feb, 2019, 11:11: PM

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