A wire of length L carries a current I. If the wire is formed into a circular loop, then the maximum torque on it in a uniform magnetic field B is

$\frac{IL^2B}{4\pi}$

For maximum torque the loop should be circular.

$ L = 2\pi R $

$ R = \frac{ L}{2\pi}$

$ \text{Area of the loop is } A = \pi R^2 = \frac{L^2}{4\pi}$

$ \text{Torque } \tau = MB = IAB = I \frac{L^2}{4\pi} B = \frac{IL^2B}{4\pi}$