Question

A conducting wire of length $l$ is turned in the form of a circular coil and a current $i$ is passed through it. For torque due to magnetic field produced at its center to be maximum, the number of turns in the coils will be

• A. $1$
• B. $2$
• C. $\infty$
• D. $0$

Answer 1

The correct option is A $1$

$\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}$
$=ni\overrightarrow{A}\times \overrightarrow{B}$
$=niAB\sin \theta$
So, for maximum torque nA should be maximum for a given length of wire. And for a given length nA is maximum for n = 1 because $nA=n\pi (\frac{l}{2n\pi }{)}^2$
$=\frac{l^2}{4n\pi }$
So, nA will be maximum for $n=1$