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

${\tau }_{max}=MB$ or ${\tau }_{max}=ni\pi a^{2}B$. Let number of turns in length l is n so $l=n\left(2\pi a\right)$ or $a=\frac{1}{2\pi n}$
$\Rightarrow {\tau }_{max}=\frac{ni\pi B{l}^2}{4{\pi }^2{n}^2}=\frac{l^{2}iB}{4\pi n_{min}}\Rightarrow {\tau }_{max}\propto \frac{1}{n_{min}}\Rightarrow n_{min}=1$