The figure below shows the north and south poles of a permanent magnet in which n turn coil of the area of cross-section A is resting, such that for a current i passed through the coil, the plane of the coil makes an angle $\theta$ with respect to the direction of magnetic field B. If the plane of the magnetic field and the coil are horizontal and vertical respectively, the torque on the coil will be:

$1. \tau =niAB\cos \theta$
$2. \tau =niAB\sin \theta$
$3. \tau =niAB$
$4. None of the above$

 

If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B, the work done in rotating the magnet through an angle is

1. $MB(1-\sin \theta )$

2. $MB\sin \theta$

3. $MB\cos \theta$

4. $MB(1-\cos \theta )$

A magnet of magnetic moment M is situated with its axis along the direction of a magnetic field of strength B. The work done in rotating it by an angle of 180^o will be

(1) -MB                        

(2) +MB

(3) 0                            

(4) +2MB

A magnetic needle is kept in a non-uniform magnetic field. It experiences:

1. A force and a torque

2. A force but not a torque

3. A torque but not a force 

4. Neither a torque nor a force

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.