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. `lBl^(2)`
B. `4pilBl^(2)`
C. `(ll^(2)B)/(4pi)`
D. zero

Answer

c

Explanation

`tau=NIAB=Npir^(2)B`
But, `Nxx2pir=I`
`:. r=I/(2piN)`
`:. Rau=NI pi(I/(2piN))^(2) B=NI pi (I^(2))/(4pi^(2)N^(2))B =(II^(2)B)/(4piN)`
`:. tau_(max)=(II^(2)B)/(4pi)` `[N_("min")=1]`