Question

A wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. If this coil is placed in a magnetic field then the torque acting on the coil will be maximum when the number of turns is

• A. as large as possible
• B. any number
• C. $2$
• D. $1$

Answer 1

The correct option is D $1$

When a loop is placed in external magnetic field,maximum torque is given by
${\tau }_{max}=MB$
Where $M$ is Magnetic moment of loop
$\Rightarrow {\tau }_{max}=ni\pi r^{2}B$.
Let number of turns in length $l$ is $n$
so
$l=n\left(2\pi r\right)$
$r=\frac{l}{2\pi n}$
${\tau }_{max}=\frac{ni\pi B{l}^2}{4{\pi }^2{n}^2}=\frac{l^{2}iB}{4\pi n_{min}}\Rightarrow {\tau }_{max}\propto \frac{1}{n_{min}}\Rightarrow n_{min}=1$.