Question

A current $I=5.0A$ flows along a thin wire shaped as shown in Fig. The radius of a curved part of the wire is equal to $R=120mm$, the angle $2\phi ={90}^{\circ }$. Find the magnetic induction of the field at the point $O$.

Answer 1

Magnetic induction due to the arc segment at $O$,
$B_{arc}=\frac{{\mu }_0}{4\pi }\frac{i}{R}(2\pi -2\phi )$
and magnetic induction due to the line segment at $O$,
$B_{line}=\frac{{\mu }_0}{4\pi }\frac{i}{R\cos \phi }\left[2\sin \phi \right]$
So, total magnetic induction at $O$,
$B_0=B_{arc}+B_{line}=\frac{{\mu }_0}{2\pi }\frac{i}{R}[\pi -\phi +\tan \phi ]=28\mu T$