A bar magnet having a magnetic moment of 2 . 0 × 10 5 J T - 1 , is placed along the direction of uniform magnetic field of magnitude B = 14 × 10 - 5 T . The work done in rotating the magnet slowly thr

Question

A bar magnet having a magnetic moment of 2 . 0 × 10 5 J T - 1 , is placed along the direction of uniform magnetic field of magnitude B = 14 × 10 - 5 T . The work done in rotating the magnet slowly through 60 ° from the direction of field is

TestHub · Accepted Answer

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

$W_{e x t} = Δ U = U_{f} - U_{i}$

$\Rightarrow W_{e x t} = - M B \cos θ_{2} + M B \cos θ_{1}$

$\Rightarrow W_{e x t} = M B (\cos θ_{1} - \cos θ_{2})$

$\Rightarrow W_{e x t} = 14 \times 10^{- 5} \times 2 \times 10^{5} (\cos 0 ° - \cos 60 °)$

$\Rightarrow W_{e x t} = 14 \times 2 \times \frac{1}{2} = 14 J$

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