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

A solenoid has a core of material with relative permeability \(400.\) The windings of the solenoid are insulated from the core and carry a current of \(2\) A. If the number of turns is \(1000\) per metre, the magnetic field intensity \(H\) is:
1. \(2\times10^2\) A/m
2. \(2\times10^3\) A/m
3. \(2\) A/m
4. \(20\) A/m

A solenoid has a core of material with relative permeability \(400.\) The windings of the solenoid are insulated from the core and carry a current of \(2~\text{A}\). If the number of turns is \(1000\) per metre, the magnetising field \(B\) is:
1. \(10~\text{T}\) 
2. \(1~\text{T}\)
3. \(0.1~\text{T}\)
4. \(2~\text{T}\)

A solenoid has a core of material with relative permeability \(400.\) The windings of the solenoid are insulated from the core and carry a current of \(2~\text{A}\). If the number of turns is \(1000\) per metre, the magnetizing current \(I_m\) is:
1. \(746~\text{A}\)
2. \(700~\text{A}\)
3. \(729~\text{A}\)
4. \(794~\text{A}\)

A domain in ferromagnetic iron is in the form of a cube of side length \(1\) µm. The maximum possible dipole moment is:
[The molecular mass of iron is \(55\) g/mole and its density is \(7.9\) g/cm³. Assume that each iron atom has a dipole moment of \(9.27\times 10^{-24}\) Am²]
1. \(8.0\times10^{-13}\) Am²
2. \(8.0\times10^{-12}\) Am²
3. \(7.0\times10^{-13}\) Am²
4. \(7.0\times10^{-12}\) Am²

When a bar magnet is rotated from its position parallel to the external magnetic field \(B=10^{-3}\) T to a direction opposite to the field (anti-parallel), the work done is \(3\) J.
Then, the maximum torque experienced by this magnet in this field is:
1. \(3\times10^{-3}\) N-m
2. \(3\times10^{3}\) N-m
3. \(6\) N-m
4. \(1.5\) N-m

Three identical bar magnets, each having dipole moment \(M,\) are placed at the origin — oriented along the x-axis, the y-axis and the z-axis respectively. The net magnetic moment of the dipoles has the magnitude:
1. \(3~M\)

2. \(\sqrt2~M\)

3. \(\sqrt3~M\)

4. \(\text{zero}\)

A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the axis of the loop is in: 

1. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
2. \(\frac{\mu_{0}}{4 \pi} \frac{\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
3. \(\frac{\mu_{0}}{4 \pi} \frac{2\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
4. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{2M}}{\mathrm{d}^{3}}\)

Choose the correct option: 
1. (a), (b) 
2. (b), (c) 
3. (c), (d) 
4. (a), (d)