Physics - Magnetism Question with Solution | TestHub

Field due to a straight wire of infinite length is $\frac{{\mu }_0\mathrm{i}}{4\pi \mathrm{r}}$ ifthe point is on a line perpendicular to its length while at the centre of a semicurcular coil is $\frac{{\mu }_0\pi i}{4\pi r}$
$$\begin{array}{l}\therefore \mathrm{B}={\mathrm{B}}_{\mathrm{a}}+{\mathrm{B}}_{\mathrm{b}}+{\mathrm{B}}_{\mathrm{c}}\\ =\frac{{\mu }_0}{4\pi }\frac{\mathrm{i}}{\mathrm{r}}+\frac{{\mu }_0}{4\pi }\frac{\pi \mathrm{i}}{\mathrm{r}}+\frac{{\mu }_0}{4\pi \mathrm{r}}\frac{\mathrm{i}}{\mathrm{r}}\\ =\frac{{\mu }_0}{4\pi }\frac{\mathrm{i}}{\mathrm{r}}(\pi +2)\text{ out of the phase }\end{array}$$