A 250-turn rectangular coil with a length of 2.1 cm and a width of 1.25 cm carries 85 \(\mu\)A and is subjected to a magnetic field with a strength of 0.85 T. What is the work done to rotate the coil by 180 degrees against the torque?

1. 9.1 $\mu J$

2. 4.55 $\mu J$

3. 2.3 $\mu$$J$

4. 1.5 $\mu J$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by \(60^{\circ}\) is \(W\). Now the torque required to keep the magnet in this new position is:
1. \(\frac{W}{\sqrt{3}}\)
2. \(\sqrt{3}W\)
3. \(\frac{\sqrt{3}W}{2}\)
4. \(\frac{2W}{\sqrt{3}}\)