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## Homework Statement

We have wires like in the picture and we want to know the value of magnetic field as

function of x:

NOTE: We want to know the magnetic field at point P ( P is on +x axis ) ( Which is totally arbitary!) The picture is there for just to give the idea.

R is the distance from each wire to point P.

## Homework Equations

[itex] H = \frac{I}{2 \pi R }[/itex]

## The Attempt at a Solution

Okey, so the currents are going in opposite ways. By the right hand rule we get the direction of the magnetic field due to each wire!

We notice that the y-component cancels out ( due to symmetry ), and that the magnetic field is only the x component due to each wire at point P.

So by superposition principle we get the magnetic field at point P on x -axis:

[itex]H = sin(\theta) \frac{ I }{ \pi R }[/itex]

Now [itex]sin(\theta)[/itex] is the angle between x axis and the distance R from each wire.

So we get from trigonometry:

[itex]H = \frac{d \cdot I }{ \pi R^2}[/itex]

[itex]H = \frac{d \cdot I }{ (x ^2 + d ^2 ) \pi }[/itex]

Not sure if this is right? At least the units match ( A / m ), but... problem is:

My assigment gives us only the current I and the x -axis distance to point P? So I assume the right answer of the

**magnetic field at point P should be independent of d**? But that doesn't make sense to me.

Sincerely yours,

Siune