Physics - Magnetism Question with Solution | TestHub

The magnetic field at $\mathrm{C}$ due to first conductor is ${\mathrm{B}}_1=\frac{{\mu }_0}{2\pi }\frac{\mathrm{I}}{3\mathrm{d}/2}$ (since, point $\mathrm{C}$ is separated by $\mathrm{d}+\frac{\mathrm{d}}{2}=\frac{3\mathrm{d}}{2}$ from 1 st conductor). The direction of field is perpendicular to the plane of paper and directed outwards. The magnetic field at $\mathrm{C}$ due to second conductor is ${\mathrm{B}}_2=\frac{{\mu }_0}{2\pi }\frac{10}{\mathrm{d}/2}$ (since, point $\mathrm{C}$ is separated by $\frac{\mathrm{d}}{2}$ from 2 nd conductor) The direction of field is perpendicular to the plane of paper and directed inwards. Since, direction of ${\mathrm{B}}_1$ and ${\mathrm{B}}_2$ at point $\mathrm{C}$ is in opposite direction and the magnetic field at C is zero, therefore, $$\begin{array}{c}{\mathrm{B}}_1={\mathrm{B}}_2\\ \frac{{\mu }_0}{2\pi }\frac{\mathrm{I}}{3\mathrm{d}/2}=\frac{{\mu }_0}{2\pi }\frac{10}{\mathrm{d}/2}\end{array}$$ On solving $\mathrm{I}=30.0\mathrm{A}$