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, $\tau_{\max }=M B$
or $\tau_{\max }=n i \pi r^{2} B$
Let number of turns in length $l$ is $n$ so $l=n(2 \pi r)$
or $r=\frac{l}{2 \pi n}$
$\Rightarrow \tau_{\max }=\frac{n i \pi B l^{2}}{4 \pi^{2} n^{2}}=\frac{l^{2} i B}{4 \pi n_{\min }}$
$\Rightarrow \tau_{\max } \propto \frac{1}{n_{\min }}$
$\Rightarrow n_{\max }=1$