A length `L` of wire carries a current `i`. Show that if the wire is formed into a circular coil, then the maximum torque in a given magnetic field is developed when the coil has one turn only, and that maximum torque has the magnitude `tau=L^2iB/4pi`

Explanation

`:'L=2piRimpliesR=L/(2pi)`
`M=iA=i(piR^2)`
`=(i)(pi)(L)/(2pi)^2=(iL^2)/(4pi)`
`tau_max=MBsin90^@=(iBL^2)/(4pi)`