Physics - Magnetism Question with Solution | TestHub

Let the length of the wire be $L$.

When the wire is bent into a circular coil of a single turn, its circumference is equal to the length of the wire. If $r$ is the radius of the coil, then $L=2\pi r$, which gives $r=\frac{L}{2\pi }$.

The area of the circular coil is $A=\pi r^2=\pi {\left(\frac{L}{2\pi }\right)}^2=\frac{L^2}{4\pi }$.

The magnetic moment of a current carrying coil is given by $M=IA$.

Substituting the value of $A$, we get $M=I\left(\frac{L^2}{4\pi }\right)$.

For a given constant current $I$, $M\propto L^2$.

Answer: $M\alpha L^2$