Magnetic Field from an Arc of Current

What is the magnetic field at the center of an arc of current of radius R? The arc curves through an angle q. 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 = (mo / 4p ) I ds ´ /r2

r = R, and ds ´ = ds

Our integral for the net field is easy:

B = ( mo I / 4pR2 ) ò ds

B = ( mo I / 4pR2 ) s

where s is the arc length, equal to Rq.

Therefore B = mo Iq / 4pR