The rectangular coil having 100 turns is placed in a uniform magnetic field of $\left(0.05\right)\widehat{j}$ Telsa as shown in figure. The torque acting on the loop is  $p\times {10}^{-3}Nm\widehat{k}$ . find $p$

The magnetic dipole moment of the current carrying coil is given by

  $\overrightarrow{M}=NIA\hat{n}$ $=100\times 0.5\times 0.08\times 0.04\widehat{i}=0.16\widehat{i}A{m}^2$
The torque acting on the coil is
 $\overrightarrow{\tau }=\overrightarrow{M}\times \overrightarrow{B}=M\left(\widehat{i}\times \widehat{j}\right)B$
 $=16\times {10}^{-2}\times 0.05\widehat{k}$
 $=8\times {10}^{-3}\left(Nm\right)\widehat{k}$.