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

Options

A. one
B. two
C. three
D. more than three

Explanation

Let n be the no. of turns formed of circular coil of radius r, in length l of the wire. Then
`l=(2pir)n`
or `r=(l)/(2pin)`
Maximum torque, `tau_(max.)=nIAB=nIpir^2B`
`=nIpixx(l//2pin^2)B=(l^2IB)/(4pin)`
`tau` will be maximum if n is minimum. If will be so if `n=1`.