A length L of a wire carries a current I. Prove that if the wise is formed into a circular loop, the maximum torque in a given magnetic field will be developed if the coil has one turn only. Find the value of the maximum torque acting on the circular coil.

Explanation

For a given length of wire, the torque on a planar loop is maximum when area enclosed by the loop is maximum. For a given length of wire, a circular loop will enclose maximum area, so we will construct a circular loop of radius r which is given by
` 2pir = 0.5`
` rArr " " r = (0.5)/(2pi) = 0.08 `m
` :. ` Area of the circular loop,
` A = pi r^(2) = 3.14 xx (0.08)^(2) = 0.02 m^(2)`
Maximum torque on the loop will be
` tau_("max") = IBA`
Here, ` I = 12A, B = 500 " gauss " = 500 xx 10^(-4) = 5 xx 10^(-2) T `
` :. " " tau_("max") = 12 xx 5 xx 10^(-2) xx 0.02`
` = 1.2 xx 10^(-2) `Nm