A bar magnet having a magnetic moment of 2 . 0 × 10 ^ 5 J T ^ - 1 ,...

Work done by the external force is equal to the change in the potential energy,

${W}_{ext} = \DeltaU = {U}_{f} - {U}_{i}$

$⇒ {W}_{ext} = - MBcos{\theta}_{2} + MBcos{\theta}_{1}$

$⇒ {W}_{ext} = MB\left(cos{\theta}_{1} - cos{\theta}_{2}\right)$

$⇒ {W}_{ext} = 14 \times {10}^{- 5} \times 2 \times {10}^{5}\left(\cos 0 ° - \cos 60 °\right)$

$⇒ {W}_{ext} = 14 \times 2 \times \dfrac{1}{2} = 14J$