Physics - Magnetism Question with Solution | TestHub

Find$\mathrm{B}$due to each arc at$\mathrm{O}$and add them using vector addition.

Since magnetic field at the centre of an arc is equal to$\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{I}}{4\mathrm{\pi r}}\mathrm{\theta }$

hence, net$\mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{i}}{4\mathrm{\pi }}\mathrm{ }\left[\frac{1}{\mathrm{R}}-\frac{1}{2\mathrm{R}}+\frac{1}{3\mathrm{R}}\right]\mathrm{\theta }=\frac{5{\mathrm{\mu }}_0\mathrm{i\theta }}{24\mathrm{\pi R}}$