A circular coil with a radius of 2.0 cm consists of 500 turns and...

Given:
Radius of the coil, $r = 2.0 \text{ cm} = 0.02 \text{ m}$
Number of turns, $N = 500$
Current, $I = 1.0 \text{ A}$
Magnetic field, $B = 0.40 \text{ T}$
Angle between the axis of the coil and the magnetic field, \theta = 30^{}^{{}^{\circ}}

The magnetic moment of the coil is given by:
$M = N I A = N I (\pi r^2)$

Substituting the values:
$M = 500 \times 1.0 \times \pi \times (0.02)^2 = 500 \times 0.0004 \pi = 0.2 \pi \text{ A m}^2$

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

Substituting the values:
\tau = 0.2 \pi \times 0.40 \times \sin 30^{}^{{}^{\circ}}
$\tau = 0.08 \pi \times 0.5$
$\tau = 0.04 \pi \text{ N m}$

Using $\pi \approx 3.14$:
$\tau \approx 0.04 \times 3.14 = 0.1256 \text{ N m} \approx 0.13 \text{ N m}$