A long magnetic needle of length \(2L\), magnetic moment \(M\) and pole strength \(m\) units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:
1. \(\frac{M}{2} , \frac{m}{2}\)
2. \(M , \frac{m}{2}\)
3. \(\frac{M}{2} , m\)
4. \(M, m\)

Two identical thin bar magnets each of length l and pole strength m are placed at the right angle to each other with the north pole of one touching south pole of the other. The magnetic moment of the system is :

1. ml

2. 2ml

3. $\sqrt{2}ml$

4. $\frac{1}{2}ml$

Rate of change of torque  with deflection is maximum for a magnet suspended freely in a uniform magnetic field of induction B, when

Force between two identical bar magnets whose centres are r metre apart  is 4.8 N, when their axes are in the same line. If separation is increased to 2r, the force between them is reduced to

1. 2.4N                         2. 1.2N

3. 0.6N                         4. 0.3N

A bar magnet of magnetic moment 10⁴J/T is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from a direction parallel to a horizontal magnetic field of 4×10^–5 T to a direction 60° from the field will be

1. 0.2 J                          2. 2.0 J

3. 4.18 J                        4. 2 × 10² J

Two equal bar magnets are kept as shown in the figure. The direction of the resultant magnetic field, indicated by arrowhead at the point \(P\) is: (approximately)

1.		2.
3.		4.

A magnet of magnetic moment $50\widehat{i }A-m^2$ is placed along the x-axis in a magnetic field $\overrightarrow{B}=(0.5\hat{i}+3.0\hat{j})T$. The torque acting on the magnet is

1. 175 $\hat{k}$ N-m

2. 150 $\hat{k}$ N-m

3. 75 $\hat{k}$ N-m

4. 25$\sqrt{37}$ $\hat{k}$ N-m

1. Intersect at the neutral point

2. Intersect near the poles of the magnet

3. Intersect on the equatorial axis of the magnet

4. Do not intersect at all

The magnetic field lines due to a bar magnet are correctly shown in

1. 

2. 

3. 

4. None of these