A wire of length 1 metre is to be wound in the form of a coil have maximum magnetic moment. The suitable number of turns among the following is

Given data: 

length l and current i

Concept used: moving charges and magnetism

Detailed solution:

$\overrightarrow{\tau }=\overrightarrow{\mathrm{M}}\times \overrightarrow{\mathrm{B}}$

$=n\overrightarrow{A}\times \overrightarrow{\mathrm{B}}$

$=ni\mathrm{ABsin}\theta$

Therefore, for a given wire length, n A should be at its highest for maximum torque and n A is for a certain length

$\mathrm{nA}=\mathrm{n}\pi {\left(\frac{l}{2\mathrm{n}\pi }\right)}^2$

$=\frac{l^2}{4n\pi }$

$\mathrm{Maximum} \mathrm{n}=1$