Magnetic field Due to a Current in a Circular Arc of Wire

We would use the equation below to write the magnitude of the field produced by a single current-length element.

The magnitude of the magnetic field at the center of a circular arc, of radius R and central angle ф  (in radians) carrying current i, is

(at center of circular arc)

(at center of full circle)

(a) A wire in the shape of a circular arc with center C carries current i.

(b) For any element of wire along the arc, the angle between the directions of     ds and ȓ is 90 degree.

(c) Determining the direction of the magnetic field at the center C due to the current in the wire , the field is out of the page , in the direction of the fingertips, as indicated by the colored dot at C.