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 = (m_o / 4p ) I ds ´ /r²

r = R, and ds ´ = ds

Our integral for the net field is easy:

B = ( m_o I / 4pR² ) ò ds

B = ( m_o I / 4pR² ) s

where s is the arc length, equal to Rq.

Therefore B = m_o Iq / 4pR