A bar magnet of length l and magnetic dipole moment M is bent to form an arc which subtends an angle of $120°$ at centre. The new magnetic dipole moment will be

1.  $\frac{3\mathrm{M}}{2\mathrm{\pi }}$

2.  $\frac{3\sqrt{3}\mathrm{M}}{2\mathrm{\pi }}$

3.  $\frac{3\mathrm{M}}{\mathrm{\pi }}$

4.  $\frac{2\mathrm{M}}{\mathrm{\pi }}$

A small bar magnet is placed with its north pole facing the magnetic north pole. The neutral points are located at a distance r from its centre. If the magnet is rotated by 180^o, the neutral point shall be obtained at a distance of:
1. \(2r\)
2. \(\sqrt{2}r\)
3. \(2^{\frac{1}{3}}r\)
4. \(\frac{r}{2\sqrt{2}}\)

The unit of pole strength is:
1. \(\text{Am}^2\)
2. \(\text{Am}\)
3. \(\frac{\text{A}^2}{\text{m}}\)
4. \(\frac{\text{A}^2}{\text{m}^2}\)

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. \(2^{\frac{-1}{3}}\)
3. \(2^{3}\)
4. \(2^{\frac{1}{3}}\)

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 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:$\sqrt{5}$

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