Physics - Magnetism Question with Solution | TestHub

Magnetic field at the centre $M$ due to current through the curved portion $DA$ is ${\vec{B}}_1=\frac{{\mu }_{0}I}{4\pi R}\times \left(\frac{3\pi }{2}\right)$ $=\frac{3{\mu }_{0}I}{8R}\otimes$ Magnetic field at the centre $M$ due to current through the straight portion $AB$ is $B_2=0$, since point $M$ lies on the axis of the straight portion $AB$. Magnetic field at the centre $M$ due to current through the curved portion $BC$ is ${\vec{B}}_3=\frac{{\mu }_{0}I}{4\pi 2R}\times \frac{\pi }{2}=\frac{{\mu }_{0}I}{16R}\otimes$ Magnetic field at the centre $M$ due to current through the straight portion $CD$ is $B_4=0$, since point $M$ lies on the axis of the straight portion $CD$. The resultant magnetic field at the point $M$ is $\begin{array}{rl}\vec{B}& ={\vec{B}}_1+{\vec{B}}_2+{\vec{B}}_3+{\vec{B}}_4\\ & =\left(\frac{3{\mu }_{0}I}{8R}+0+\frac{{\mu }_{0}I}{16R}+0\right)\otimes =\frac{7{\mu }_{0}I}{16R}\otimes \end{array}$