A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of magnetic induction along its axis is

Given data

Current $=I$

Radius $=R$

Concepts used moving charges and magnetism

Explanation

Elementary length dl is cut for magnetic field

$dL=Rd\theta$

Magnetic field

$B={\int }_0^{\pi }dB\sin \theta d\theta =2dB$

By solving we get

$B=\frac{{\mu }_{0}I}{{\pi }^{2}R}$