Please do it fast

Please do it fast 3) +0.064J, -0.128J 4) 0.0321 12. When a bar magnetis placed at 900 to uniform magnetic field, it is acted upon by a couple which is maximum. For the couple to be halfof the maximum value, it is to be inclined to the magnetic field at an angle is 1) 300 2) 450 3) 600 4) 900

Dear Student,
Let us consider a bar magnet of length 2l and pole strength m. Then its magnetic moment is M = 2ml.
If the magnet is placed in a uniform magnetic field, then the couple acting on the bar magnet is:
$\tau = M\times B = MB\sin \theta$, where, ϴ is the angle made by the magnet with the external magnetic field.
The couple will be maximum at ϴ=90 while the couple will be half the maximum value at $\sin \theta =\frac{1}{2}$.
Therefore, $\theta ={\sin }^{-1}\left(\frac{1}{2}\right) = {30}^o$. Ans (1)
Regards,