Let 2 long parallelwires a distance d apart carry currents in the oppositedirect

Question

Let 2 long parallelwires a distance d apart carry currents in the oppositedirection. One wire is at x=0 and has a current 2I (out ofthe page). The other wire is at x=d and carries a currentI (out of the page). Determine the magnetic field B alongthe x axis between the wires as a function of x.
Please show all steps fully and give a final answer,thanks!! Let 2 long parallelwires a distance d apart carry currents in the oppositedirection. One wire is at x=0 and has a current 2I (out ofthe page). The other wire is at x=d and carries a currentI (out of the page). Determine the magnetic field B alongthe x axis between the wires as a function of x.
Please show all steps fully and give a final answer,thanks!! Please show all steps fully and give a final answer,thanks!!

Explanation / Answer

let p be a point at a distance a from the wire at x = 0,themagnetic field due to the wire is B1 =(oI1/2a) o = 4 * 10-7 N/A2and I1 = 2I and B2 = (oI2/2 *(d - a)) I2 = I The magnetic field due to wire 1 is counter clockwise.This isbecause according to Ampere's right hand thumb rule,when the thumbof the right hand points in the direction of the current flow thenthe curling of fingers indicates the direction of the magneticfield.The current due to wire 1 is pointing outside of the pagetherefore,the magnetic field due to this wire is counterclockwise.Similarly,the magnetic field due to the wire 2 isclockwise.We take the counter clockwise magnetic field as positiveand the clockwise magnetic field as negative.Therefore,the magneticfield B along the x axis between the wires as a function of xis B = B1 + B2 or B = (oI1/2a) +(-(oI2/2 * (d - a))) =(oI1/2a) -((oI2/2 * (d - a)) or B = (o/2) *[(I1/a) - (I2/(d - a))] =(o/2) * [(2I/a) - (I/(d - a))] or B = (oI/2) * (2d - 3a/d - a) or B = (oI1/2a) +(-(oI2/2 * (d - a))) =(oI1/2a) -((oI2/2 * (d - a)) or B = (o/2) *[(I1/a) - (I2/(d - a))] =(o/2) * [(2I/a) - (I/(d - a))] or B = (oI/2) * (2d - 3a/d - a)

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