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## Homework Statement

When I use Biot-Savart law to calculate the magnetic field at a distance from an arc, I get the well known

[tex]B=\frac{i\mu_{0}\phi}{4 \pi R}[/tex]

Why can't I use Amperes law for this? I could imagine that the arc instead to be a complete loop of current. Then I could find the B inside the loop using Amperes law, and then multiply this simply by the [tex]\frac{arc angle}{360}[/tex], since I see superposition used for B fields.

I smell a rat in the

*"I could find the B inside the loop using Amperes law"*part though... Things cancel out that should not cancel out. But I don't get it intuitively...