Which of the following statement is incorrect?

(1) If a bar magnet is cut into two pieces transverse to its length and along its length, in either case, one gets two magnets, each with a north and south pole.

(2) A magnetized needle in a uniform magnetic field experiences a torque but no net force. An iron nail near a bar magnet, however, experiences a force of attraction in addition to torque.

(3) Every magnetic configuration must have a north pole and a south pole.

(4) In a bar magnet, the intensity of the magnetic field is the strongest at the two ends (poles) and weakest at the central region.

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