Two semiinfinite wires are on the same plane The wires make

Two semi-infinite wires are on the same plane. The wires make an angle of 45degree with each other and are joined by an arc of a circle of radius R. The wires carry a current I. Find the magnetic field at the center of curvature of the arc.

Solution

Here ,

theta = 45 degree

at the centre of the arc

as the magnetic field due to semi infinite wires on the line of current is zero

net magnetic field = u0 * I/(2R) * (45/360)

net magnetic field = u0*I/(16 *R)

the net magnetic field is u0*I/(16 *R)