# Biot Savart polygon with n edges

1. Jul 21, 2011

### Lindsayyyy

1. The problem statement, all variables and given/known data

I want to calculate the magnetic field with Biot Savart in the given drawing in the point P=(0,0,0)

2. Relevant equations

Biot Savart

3. The attempt at a solution

I have already problems in parametrizising the conducter loop. Can anyone give me some hints on how to do this?

Thanks for the help.

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2. Jul 21, 2011

### mathfeel

Just break the polygon into each segments, and compute the magnetic field at the origin due to each segment and add them up. It is clear the contribution from each segment is the same. So in fact, all you need is compute from one segment, then multiply by 8.

Let's pick one, say the one on the left side labeled by the I. You can parametrize points on the segment by its polar angle $(-l, l \sin \vartheta)$ to where $\sin \frac{7\pi}{8} \le \vartheta \le \sin \frac{9\pi}{8}$.
Write out at each $\vartheta$: What it the distance to origin? What is the result of $d\mathbf{l} \times \mathbf{\hat{r}}$ as a function of $\vartheta$.

Then just plug these into Biot-Savart and integrate away.

3. Jul 22, 2011

### Lindsayyyy

Thanks for your help, but how do you get to 7pi/8 etc?

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