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dingo_d
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Homework Statement
I have a regular 6 sided polygon shaped loop through which flows steady current. I have to find the field at the center, at one of the vertex of the polygon and at the great distance from the loop.
Homework Equations
Biot-Savart law:
[tex]\vec{B}=\frac{1}{c}I\int\frac{d\vec{\ell}'\times\hat{r}}{r^2}[/tex]
in CGS units.
The Attempt at a Solution
So I found the field at the center, there is a similar problem in Griffiths. And I got:
[tex]B=\frac{6 I}{c a}[/tex] where a is the length of a side of a polygon. Because the field for a wire is:
[tex]B=\frac{I}{cs}(\sin\theta_2-\sin\theta_1)[/tex], s=a and [tex]\theta_2=-\theta_1=\frac{\pi}{6}[/tex]. And I multiply by 6 because I have 6 sides.
Now I am not sure if this next part is correct and I need some help with it:
At the vertex the field will be 0? Am I correct? Because the element of the wire is in the same direction as the vector from the source (the wire) to the point in which I'm looking at the field (the vertex).
The last part is the confusing one. Now I read that B-S law is sth like Coulomb law, but for currents and magnetostatics, that is it's inverse square law. That means that it falls as I'm getting away from the source.
When I had, in electrostatics, case with uniformly charged sphere when at great distance I'd get the field that is the same as the field for the single point charge.
But what do I get for this? Since it's closed loop, I certainly can't get the answer for infinite wire. Do I get the field of a magnetic field of a circular loop?