Physics - Magnetism Question with Solution | TestHub

The magnetic field at O is the sum of contributions from the semi-circular arc and the straight wire.

For the semi-circular arc: $B_1=\frac{{\mu }_{0}I}{4r}$.

For the straight wire: $B_2=\frac{{\mu }_{0}I}{4\pi r}$.

Both fields are directed into the page.

Total magnetic field: $B=B_1+B_2=\frac{{\mu }_{0}I}{4r}+\frac{{\mu }_{0}I}{4\pi r}$.