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

Answer: (D)

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