Question

A circular coil of magnetic moment 10 Am² is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A uniform magnetic field of 2 T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90 degrees under the influence of the magnetic field. What are the magnitudes of the torques on the coil in the initial and final positions?

Answer 1

Dear Student,

$$\begin{gathered} \mathrm{\tau }=\left|\mathrm{m}\times \mathrm{B}\right| \\ \mathrm{where},\mathrm{m}=\mathrm{magnetic}\mathrm{moment} \\ \mathrm{B}=\mathrm{magnetic}\mathrm{field} \\ \mathrm{\tau }=\mathrm{mB}\mathrm{sin\theta } \\ \mathrm{Initially},\mathrm{\theta }=0°. \\ \mathrm{Thus},\mathrm{initial}\mathrm{torque},{\mathrm{\tau }}_1=0 \\ \mathrm{Finally},\mathrm{\theta }=90° \\ \mathrm{Final}\mathrm{torque},{\mathrm{\tau }}_{\mathrm{f}}=\mathrm{mB} \\ {\mathrm{\tau }}_{\mathrm{f}}=10\times 2=20\mathrm{N}-\mathrm{m} \end{gathered}$$