A rectangular coil of size 3.0 cm 4.0cm and having 100 turns, is pivoted about the z-axis as shown in figure . The coil carries an electric current of 2.0 A and a magnetic field of 1.0 T is present along the y-axis. Find the torque acting on the coil if the side in the x-y plane makes an angle $\mathrm{\theta }=37°$  with the x-axis. (Take$\sin {37}^{\circ }=0.6$  )
 

The magnetic moment of the loop is $\overrightarrow{\mathrm{\mu }}=\mathrm{ni}\overrightarrow{\mathrm{A}}$ where n is the number of turns, i is the current and $\overrightarrow{\mathrm{A}}$ is the area-vector. The direction of $\overrightarrow{\mathrm{A}}$  is determined by the sense of the  current and in this case it lies in the fourth quadrant making an angle $\mathrm{\theta }=37°$ with the  negative y-axis. Torque  $\overrightarrow{\mathrm{\Gamma }}=\overrightarrow{\mathrm{\mu }}\times \overrightarrow{\mathrm{B}}=\mathrm{ni}\overrightarrow{\mathrm{A}}\times \overrightarrow{\mathrm{B}}$
Thus,   $\mathrm{\Gamma }=100\times \left(2\mathrm{A}\right)\times \left(12\times {10}^{-4}{\mathrm{m}}^2\right)\times 1\mathrm{T}\times \sin {37}^0=0.144\mathrm{Nm}$
The torque is along the positive z-axis.