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

Two small bar magnets are placed in the air at a distance r apart. The magnetic force between them is proportional to:
(1) $r^2$
(2) $r^{-2}$
(3) $r^{-3}$
(4) $r^{-4}$

A short magnetic dipole is placed at the origin with its dipole movement directed along the +x-axis. If magnetic field induction at a point P (r, 0) is \(B\hat{i}\), the magnetic field induction at point Q (0, 2r) will be:
1. \(-\frac{B}{16}\hat{i}\)
2. \(-\frac{B}{8}\hat{j}\)
3. \(\frac{B}{16}\hat{j}\)
4. \(-\frac{B}{16}\hat{j}\)

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 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. 

Points A and B are situated perpendicular to the axis of a 2cm long bar magnet at large distances X and 3X from its centre on opposite sides. The ratio of the magnetic fields at A and B will be approximately equal to
(a) 1 : 9               (b) 2 : 9
(c) 27 : 1             (d) 9 : 1

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. $MB(1-\cos \theta )$

Two small bar magnets are placed in a line with like poles facing each other at a certain distance d apart. If the length of each magnet is negligible as compared to d, the force between them will be inversely proportional to
1. d
2. d²
3. $\frac{1}{d^2}$
4. $d^4$
 

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 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

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 straight wire carrying a current i is turned into a circular loop. If the magnitude of the magnetic moment associated with it in M.K.S. unit is M, the length of wire will be
1. $4\mathrm{\pi iM}$                          2. $\sqrt{\frac{4\mathrm{\pi M}}{i}}$
3. $\sqrt{\frac{4\mathrm{\pi i}}{M}}$                        4. $\frac{M\mathrm{\pi }}{4i}$

Two similar bar magnets P and Q, each of magnetic moment M, are taken. If P is cut along its axial line and Q is cut along its equatorial line, all the four pieces obtained have:

Two bar magnets with magnetic moments 2 M and M are fastened together at right angles to each other at their centres to form a crossed system, which can rotate freely about a vertical axis through the centre. The crossed system sets in earth’s magnetic field with magnet having magnetic moment 2M making an angle $\theta$ with the magnetic meridian such that
(a) $\theta ={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$            (b) $\theta ={\tan }^{-1}\left(\sqrt{3}\right)$
(c) $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)$               (d) $\theta ={\tan }^{-1}\left(\frac{3}{4}\right)$

A magnetic needle suspended by a silk thread is vibrating in the earth's magnetic field. If the temperature of the needle is increased by 500°C, then
(1) The time period decreases
(2) The time period remains unchanged
(3) The time period increases
(4) The needle stops vibrating

A superconductor exhibits perfect :
(1) Ferrimagnetism              
(2) Ferromagnetism
(3) Paramagnetism              
(4) Diamagnetism

Two short magnets of equal dipole moments M are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is :

1. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{M}{d^3}$
2. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{M\sqrt{2}}{d^3}$
3. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{2\sqrt{2}M}{d^3}$
4. $\frac{{\mu }_0}{4\mathrm{\pi }} \frac{2M}{d^3}$