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**Adding two magnetic forces**

## Homework Statement

Well, it's kinda stupid, but I've truely forgot how to do this.

I've got 3 infinite long wires that is located as in this image:

http://www.gratisupload.dk/download/41857/" [Broken]

where the wires is, ofc, inifinite.

Well, I have to calculate the force acting on wire 1 from wire 2 and 3.

And the current running through the wires are as stated in the picture.

## Homework Equations

[tex]\frac{F}{L}=\frac{{{\mu }_{0}}II'}{2\pi r}[/tex]

## The Attempt at a Solution

So I calculate the force from wire 2 to wire 1, and from wire 3 to wire 1, which gives:

[tex]\frac{{{F}_{2-1}}}{L}=\frac{{{\mu }_{0}}I\left( -2I \right)}{2\pi a}=\frac{-{{\mu }_{0}}{{I}^{2}}}{\pi a}[/tex]

and

[tex]\frac{{{F}_{3-1}}}{L}=\frac{{{\mu }_{0}}II}{2\pi \left( \sqrt{{{a}^{2}}+{{a}^{2}}} \right)}=\frac{{{\mu }_{0}}{{I}^{2}}\sqrt{2}}{4\pi a}[/tex]

My problem is, that I know that the total force is just not by adding the two expressions, but I need to do it vectorstyle - I think.

And the only way I can think of is:

[tex]\frac{{{F}_{tot}}}{L}=\sqrt{{{\left( \frac{{{F}_{2-1}}}{L} \right)}^{2}}+{{\left( \frac{{{F}_{3-1}}}{L} \right)}^{2}}}[/tex]

But that doesn't give the right result, which should be:

[tex]{{F}_{tot}}=\frac{\sqrt{10}{{\mu }_{0}}{{I}^{2}}L}{4\pi a}[/tex]

So what am I doing wrong? I've been looking through my book, but I haven't found anything that could solve this for me. And if I'm correct it's pretty simple, but even so, I just can't remember it or figure it out...

So can anyone give me a hint?

Regards

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