Find the magnetic field at the point P in figure. The curved...

Magnitude of magnetic field due to semi-infinite portion of wire AB at point C is

${B}_{1} = \dfrac{{\mu}_{0}i}{4\pir}$

Magnitude of magnetic field due to semicircular arc BD at point C is

${B}_{2} = \dfrac{{\mu}_{0}i}{4r}$

Magnitude of magnetic field due to semi-infinite portion DE at point C is 0.

Using right-hand rule, it can be seen that directions of $\overset{\to}{{B}_{1}}$ and $\overset{\to}{{B}_{2}}$ are both outwards from the plane.

Therefore, the magnitude of net magnetic field at point C is

$B = {B}_{1} + {B}_{2}$

$= \dfrac{{\mu}_{0}i}{2r}\left[\dfrac{1}{2} + \dfrac{1}{2\pi}\right]$