$A$ magnet of magnetic moment $4 \, A-m^2$ is held in a uniform magnetic field $5 \times 10^{-4} \, T$ with the magnetic moment vector making an angle $30^{\circ}$ with the field. Calculate the work done in increasing the angle from $30^{\circ}$ to $45^{\circ}$.

• A
  $3.2 \times 10^{-4} \, J$
• B
  $1.6 \times 10^{-4} \, J$
• C
  $1.6 \times 10^{-3} \, J$
• D
  $3.2 \times 10^{-3} \, J$