Physics - Magnetism Question with Solution | TestHub

Length of the wire is $L$.

When bent into a circular coil of a single turn, the circumference is $2\pi R=L$.

Radius of the coil is $R=\frac{L}{2\pi }$.

Area of the coil is $A=\pi R^2=\pi {\left(\frac{L}{2\pi }\right)}^2=\frac{L^2}{4\pi }$.

Magnetic dipole moment of the coil is $M=IA=\frac{I{L}^2}{4\pi }$.

Maximum torque on the coil in a magnetic field $B$ is ${\tau }_{\text{max}}=MB$.

${\tau }_{\text{max}}=\frac{L^{2}IB}{4\pi }$.

Answer: $\frac{{\mathrm{L}}^2\mathrm{IB}}{4\pi }$