A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is :

1. 0                           2. 45°

3. 60°                       4. 90°

$1.<mspace\; width="1em"></mspace>\tau =niAB\cos \theta$
$2.<mspace\; width="1em"></mspace>\tau =niAB\sin \theta$
$3.<mspace\; width="1em"></mspace>\tau =niAB$
$4.<mspace\; width="1em"></mspace>None<mspace\; width="1em"></mspace>of<mspace\; width="1em"></mspace>the<mspace\; width="1em"></mspace>above$

Two short magnets with their axes horizontally perpendicular to the magnetic meridian are placed with their centres 40 cm east and 50 cm west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments  is

1. 4:5

2. 16:25

3. 64:125

4. 2:$\sqrt{5}$

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. $\frac{1}{2}ml$

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.