In the figure, the magnetic needle has a magnetic moment of 6.7 × 10^–2 Am² and a moment of inertia I = 7.5 × 10^–6 kg m². It performs 10 complete oscillations in 6.70 s in a magnetic field. What is the magnitude of the magnetic field?

1. 0.02 T

2. 0.01 T

3. 003 T

4. 0.001 T

A short bar magnet placed with its axis at 30° with an external field of 800 G experiences a torque of 0.016 Nm. What is the magnetic moment of the magnet?

$$\begin{gathered} 1. 0.80 A m^2 \\ 2. 0.40 A m^2 \\ 3. 0.29 A m^2 \\ 4. 0.60 A m^2 \end{gathered}$$

A short bar magnet placed with its axis at 30° with an external field of 800 G experiences a torque of 0.016 N-m. What is the work done in moving it from its most stable to the most unstable position?

1. 0.036 J

2. 0.016 J

3. 0.064 J

4. 0

A solenoid of cross-sectional area $2\times {10}^{-4} m^2$ and 1000 turns placed with its axis at 30° with an external field of 800 G experiences a torque of 0.016 Nm. The current flowing through the solenoid is:

1. 2 A

2. 4 A

3. 1 A

4. 5 A

The ratio of the magnitudes of the equatorial and axial fields due to a bar magnet of length 5.0 cm at a distance of 50 cm from its mid-point is:
(Given, the magnetic moment of the bar magnet is \(0.40~Am^{2}.\)${\mathrm{}}^{}$)
1. \(\frac{1}{2}\)
2. \(2\)
3. \(1\)
4. \(\frac{3}{2}\)

The figure shows a small magnetized needle P placed at a point O. The arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientations of the magnetic moment) of another identical magnetized needle Q. Then:

(1) In $P{Q}_1 and P{Q}_2$ configuration, the system is not in equilibrium.

(2) In $P{Q}_3 and P{Q}_6$configuration, the system is unstable.

(3) In $P{Q}_5 and P{Q}_4$ configuration, the system is stable.

(4) $P{Q}_5$ configuration corresponds to the lowest potential energy among all the configurations shown.

Which of the following is the correct representation of magnetic field lines?

1. (g), (c)

2. (d), (f)

3. (a), (b)

4. (c), (e)

Which one of the following is correct?

The earth’s magnetic field at the equator is approximately 0.4 G. The earth’s dipole moment is:
(Radius of earth, \(R_{E}=6.4\times10^{6} \) m)
1. \(1.05\times10^{23}\)$\mathrm{}$ A-m²
2. \(8.0\times10^{22}\) A-m²
3. \(4.5\times10^{23}\) A-m²
4. \(2.10\times10^{23}\) A-m²

In the magnetic meridian of a certain place, the horizontal component of the earth’s magnetic field is 0.26G and the dip angle is 60°. The magnetic field of the earth at this location is:

1. 0.25 G

2. 0.20 G

3. 0.35 G

4. 0.52 G