- #1

fluidistic

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## Homework Statement

I set up myself to derive the formula of the magnetic field due to a current I carried by an infinite wire. At a point P situated at a distance d from the wire.

## Homework Equations

Ampere's law and Biot-Savart's law.

## The Attempt at a Solution

With Ampere's law, it's simple: [tex]\oint \vec B d\vec l = \mu _0 I[/tex], thus [tex]B=\frac{\mu _0 I}{2 \pi d}[/tex] and its direction is easy to figure out thanks to the right hand rule.

I'm having problems with Biot and Savart's law.

[tex]d\vec B =\frac{\mu _0}{4\pi} I d\vec l \times \frac{\vec r}{r^3}\Rightarrow \vec B=\frac{\mu _0}{4 \pi} \oint I d\vec l \times \frac{\vec r}{r^3}[/tex], thus [tex]B=\frac{\mu _0 I}{4 \pi d}[/tex]. I don't see how I can get a factor 2 in this result, to make it coincide with the anterior result.

Aside question: If I understand well, an infinitesimal length dl of the wire contributes to the magnetic field only in an orthogonal plane to it, right? So that it doesn't contribute to points out of this plane, right?

Thanks for all.