The magnetic field at a point x on the axis of a small bar magnet is equal to the field at a point y on the equator of the same magnet. The ratio of the distances of x and y from the centre of the magnet is:
1. $2^{-3}$

2. $2^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

3. $2^3$

4. $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

A magnet of magnetic moment 20 C.G.S. units are freely suspended in a uniform magnetic field of intensity 0.3 C.G.S. units. The amount of work done in deflecting it by an angle of ${30}^o$ in C.G.S. units is
(1) 6

(2) $3\sqrt{3}$

(3) $3(2-\sqrt{3})$

(4) 3

The magnetic field due to a short magnet at a point on its axis at a distance X cm from the middle point of the magnet is 200 Gauss. The magnetic field at a point on the neutral axis at a distance of X cm from the middle of the magnet is:

1. 100 Gauss

2. 400 Gauss

3. 50 Gauss

4. 200 Gauss

A sensitive magnetic instrument can be shielded very effectively from outside magnetic fields by placing it inside a box of
1. Teak wood
2. Plastic material
3. Soft iron of high permeability
4. A metal of high conductivity

A uniform magnetic field, parallel to the plane of the paper existed in space initially directed from left to right. When a bar of soft iron is placed in the field parallel to it, the lines of force passing through it will be represented by

1. 

2.  

3. 

4. 

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 :

a) 0                           (b) 45°

(c) 60°                       (d) 90°

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

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