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A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from 
1. The current source
2. The magnetic field
3. The induced electric field due to the changing magnetic field
4. The lattice structure of the material of the rod

A 250-Turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $\mathrm{\mu }$A and subjected to a magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is 
1. 9.1 $\mathrm{\mu }$J 
2. 4.55 $\mathrm{\mu }$J 
3. 2.3 $\mathrm{\mu }$J 
4. 1.15 $\mathrm{\mu }$J

If ${\mathrm{\theta }}_1$ and ${\mathrm{\theta }}_2$ be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip $\mathrm{\theta }$ is given by
1. ${\cot }^2\mathrm{\theta }={\cot }^2{\mathrm{\theta }}_1+{\cot }^2{\mathrm{\theta }}_2$
2. ${\tan }^2\mathrm{\theta }={\tan }^2{\mathrm{\theta }}_1+{\tan }^2{\mathrm{\theta }}_2$
3. ${\cot }^2\mathrm{\theta }={\cot }^2{\mathrm{\theta }}_1-{\cot }^2{\mathrm{\theta }}_2$
4. ${\tan }^2\mathrm{\theta }={\tan }^2{\mathrm{\theta }}_1-{\tan }^2{\mathrm{\theta }}_2$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state.The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is
1. $\frac{\mathrm{W}}{\sqrt{3}}$
2. $\sqrt{3}\mathrm{W}$
3. $\frac{\sqrt{3}\mathrm{W}}{2}$
4. $\frac{2\mathrm{W}}{\sqrt{3}}$
 

The magnetic susceptibility is negative for 
1. Paramagnetic and ferromagnetic materials 
2. Diamagnetic material only
3. Paramagnetic material only 
4. Ferromagnetic material only

Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment $\overrightarrow{\mathrm{m}}$ . Which configuration has highest net magnetic dipole moment ?

1. a
2. b
3. c
4. d

A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be-

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

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It
1. Will stay in north-south direction only
2. Will stay in east-west direction only
3. Will become rigid showing no movement
4. Will stary in any position

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3}$ J of work to turn it through 60°. The torque needed to maintain the needle in this position will be
1. $2\sqrt{3} \mathrm{J}$
2. 3 J
3. $\sqrt{3} \mathrm{J}$
4. $\frac{3}{2}\mathrm{J}$

There are four light-weight-rod samples, A, B, C, D separately suspended by threads. A bar magnet is slowly
brought near each sample and the following observations are noted
i) A is feebly repelled
ii) B is feebly attracted
iii) C is strongly attracted
iv) D remains unaffected
Which one of the following is true? 
1. A is of a non-magnetic material
2. B is of a paramagnetic material
3. C is of a diamagnetic material
4. D is of a ferromagnetic material

A short bar magnet of magnetic moment 0.4 JT^–1 is placed in a uniform magnetic field of 0.16 T. The magnet
is in stable equilibrium when the potential energy is 
1. – 0.082 J           2. 0.064 J 
3. – 0.064 J           4. Zero

Electromagnets are made of soft iron because soft iron has 
1. High retentivity and low coercive force
2. Low retentivity and high coercive force
3. High retentivity and high coercive force
4. Low retentivity and low coercive force

A vibration magnetometer placed in magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 s in earth's horizontal magnetic field of 24 microtesla. When a horizontal field of 18 microtesla is produced opposite to the earth's field by placing a current carrying wire, the new time
period of magnet will be: 
1. 4 s                   2. 1 s
3. 2 s                   4. 3 s

A closely wound solenoid of \(2000\) turns and area of cross-section \(1.5\times10^{-4}\) m² carries a current of \(2.0\) A. It is suspended through its center and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field \(5\times 10^{-2}\) tesla making an angle of \(30^{\circ}\) with the axis of the solenoid. The torque on the solenoid will be:
1. \(3\times 10^{-3}\) Nm 
2. \(1.5\times 10^{-3}\) Nm 
3. \(1.5\times 10^{-2}\) Nm 
4. \(3\times 10^{-2}\) Nm

Two short bar magnets of magnetic moments 'M' each are arranged at the opposite corners of a square of side 'd', such that their centres coincide with the corners and their axes are parallel to one side of the square. If the like poles are in the same direction, the magnetic induction at any of the other corners of the square is
1. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{\mathrm{M}}{{\mathrm{d}}^3}$
2. $\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\frac{2\mathrm{M}}{{\mathrm{d}}^3}$
3. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{\mathrm{M}}{{\mathrm{d}}^3}$
4. $\frac{{\mathrm{\mu }}_0}{2\mathrm{\pi }}\frac{2\mathrm{M}}{{\mathrm{d}}^3}$

A : If a bar magnet is cut into two equal halves then magnetic dipole moment of each part is half that of theoriginal magnet.
R : Magnetic dipole moment is the product of pole strength and magnetic length.

A : A magnetized needle in a uniform magnetic field experiences a torque but no net force, however, an iron nail near a bar magnet experiences a force of attraction as well as torque.
R : Bar magnet creates non-uniform magnetic field.

A: Every magnetic configuration need not have a north pole and south pole.
R: North pole, south pole exists only if the source of the field has a net magnetic dipole moment.

A : If different ends of two identical looking iron bars are brought closer and they always attract each other then one of the bars is not magnetized.
R : Repulsion is the sure check of presence of magnetization of both the bars.

A : The magnetic field lines also represent the lines of force on a moving charged particle at every point.
R : Force on a moving charge acts parallel to the magnetic field.