A circular loop carrying a current i is made of wire with a total...

Let the radius of the circular loop be $r$.

The total length of the wire is $L$, so $2\pi r = L \Rightarrow r = \dfrac{L}{2\pi}$

The area of the circular loop is $A = \pi r^2 = \pi \left(\dfrac{L}{2\pi}\right)^2 = \dfrac{L^2}{4\pi}$

The magnetic dipole moment of the loop is $M = iA = \dfrac{i L^2}{4\pi}$

Since the magnetic field $B$ is parallel to the plane of the loop, the angle between the magnetic moment vector (which is perpendicular to the plane) and the magnetic field is $\theta = 90^{{}^{{}^{\circ}}}$

The torque acting on the loop is $\tau = M B \sin \theta$

$\tau = \left(\dfrac{i L^2}{4\pi}\right) B \sin 90^{{}^{{}^{\circ}}} = \dfrac{i L^2 B}{4\pi}$