A magnetic needle suspended parallel to a magnetic field requires \(\sqrt{3}~\text{J}\) of work to turn it through $\mathrm{}$\(60^\circ\). The torque needed to maintain the needle in this position will be:
1. \(3\) N-m
2. \(\sqrt{3} \) N-m
3. \(\frac32\) N-m
4. \(2\sqrt{3}\) N-m

A short bar magnet of magnetic moment \(0.4~\text {J/T}\) is placed in a uniform magnetic field of \(0.16~\text T.\) The magnet is in stable equilibrium when the potential energy is:
1. \(0.064~\text J\)
2. zero
3. \(-0.082~\text J\) 
4. \(-0.064~\text J\) 

A closely wound solenoid of \(2000\) turns and area of cross-section \(1.5\times10^{-4}\) m² carries a current of \(2.0\) A. It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field \(5\times 10^{-2}\) tesla making an angle of \(30^{\circ}\) with the axis of the solenoid. The torque on the solenoid will be:
1. \(3\times 10^{-3}\) Nm 
2. \(1.5\times 10^{-3}\) Nm 
3. \(1.5\times 10^{-2}\) Nm 
4. \(3\times 10^{-2}\) Nm

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:

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. \(\frac{2 W}{\sqrt{3}}\)

The magnetic field at the centre of a circular loop of area \(A\) is \(B.\) The magnetic moment of the loop is:

A current-carrying loop placed in a magnetic field behaves like a:
1. magnetic dipole
2. magnetic substance
3. magnetic pole
4. all are true