μo I dl × 
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| 4π r2 |
What is the magnetic field at the center of an arc of current of radius R? The arc curves through an angle θ. If the current is counter-clockwise the magnetic field at the center is out of the page.
The magnetic field dB from a representative piece of the wire is:
| dB | = |
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r = R, and dl × = dl 
Our integral for the net field is easy:
| B | = |
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∫ | dl |
| B | = |
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where s is the arc length, equal to Rθ.
| Therefore | B | = |
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