A circular coil having N turns is made from a wire L meter long. If a current of I ampere is passed through this coil suspended in a uniform magnetic field of B tesla, find the maximum torque that can act on this coil.

Options

A. `(BIL^(2))/(2piN)`
B. zero
C. `(BIL^(2))/(4piN)`
D. `(BIL^(2))/(8pi^(2)N)`

Answer

C

Explanation

A coil having N turns is made from the wire having length L m. Radius of this coil = R.
Numbers of turns in `2piR` length = 1
`therefore` Numbers of turns in L length = `L/(2piR)=N`
`thereforeR=L/(2piN)`
Area of cross section of coil A = `piR^(2)`
`thereforeA=(piL^(2))/(4pi^(2)N^(2))=L^(2)/(4piN^(2))`
Torquc produced in coil after passing current through it is,
`tau=NIAB=(NIL^(2)B)/(4piN^(2))`
`thereforetau=(IL^(2)B)/(4piN)Nm`