A wire of length l is bent in the form a circular coil of some turns. A current I flows through the coil. The coil is placed in a uniform magnetic field B. The maximum torqur on the coil can be

Options

A. `(iBl^(2))/(4pi)`
B. `(iBl^(2))/(pi)`
C. `(iBl^(2))/(2pi)`
D. `(2iBl^(2))/(pi)`

Answer

A

Explanation

Let `N` be the number turns and `R` the redius of the coil.
Then, `l=2piRN`
or `R=l/(2piN) …(i)`
Now magnetic moment of the coil is
`M=NiA=Ni(piR^(2))`
`=(Nipi)(l/(4pi^(2)N^(2)))=(il^(2))/(4piN)`
Maximum value of `M` can be
`M_(max)=(il^(2))/(4pi) at N=1`
`:. tau_(max)=M_(max)B sin 90^(@)=(iBl^(2))/(4pi)`.