1. What happens to the force between magnetic poles when their pole strength and the distance between them are both doubled?
Correct Answer: c) Force decreases to half the previous value
The force between two magnetic poles is given by \( F = \frac{m_1 m_2}{4\pi\mu r^2} \).
If both pole strengths (\(m_1\) and \(m_2\)) and distance (\(r\)) are doubled, the new force becomes:
\( F' = \frac{(2m_1)(2m_2)}{4\pi\mu (2r)^2} = \frac{4m_1m_2}{16\pi\mu r^2} = \frac{1}{4}F \times 2 = \frac{1}{2}F \).
Thus, the force decreases to half the previous value.
2. Magnetic field intensity is defined as
Correct Answer: b) Magnetic induction force acting on a unit magnetic pole
Magnetic field intensity (H) is defined as the force experienced by a unit north pole placed in the magnetic field.
It is measured in amperes per meter (A/m) in SI units.
3. A current loop placed in a magnetic field behaves like a
Correct Answer: a) Magnetic dipole
A current loop behaves as a magnetic dipole because it has a north and south pole.
The magnetic dipole moment (\( \vec{m} \)) is given by \( \vec{m} = I\vec{A} \),
where \( I \) is the current and \( \vec{A} \) is the area vector of the loop.
4. Points A and B are situated along the extended axis of 2 cm long bar magnet at a distance x and 2x cm respectively from the pole nearer to the points. The ratio of the magnetic field at A and B will be
Correct Answer: c) 8 : 1 exactly
The magnetic field along the axial line of a bar magnet is given by \( B = \frac{\mu_0}{4\pi} \frac{2Mr}{(r^2 - l^2)^2} \),
where \( M \) is the magnetic moment, \( r \) is the distance from the center, and \( 2l \) is the length of the magnet.
For point A at distance \( x \), and point B at distance \( 2x \), the ratio becomes \( \frac{B_A}{B_B} = \frac{(4x^2 - l^2)^2}{2(x^2 - l^2)^2} \).
For \( l \ll x \), this simplifies to \( \frac{B_A}{B_B} \approx \frac{(4x^2)^2}{2(x^2)^2} = \frac{16}{2} = 8 \).
5. The magnetic susceptibility of a paramagnetic material is
Correct Answer: a) Small and positive
Paramagnetic materials have a small positive magnetic susceptibility (\( 0 < \chi \ll 1 \)).
They are weakly attracted by magnetic fields and align their magnetic moments with the applied field.
6. The magnetism of magnet is due to
Correct Answer: a) The spin motion of electron
The magnetism of materials arises primarily from the spin motion of electrons and their orbital motion around the nucleus.
In ferromagnetic materials, the alignment of these electron spins creates a net magnetic moment.
7. The magnetic field due to a short magnet at a point on its axis at 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 X cm from the middle of the magnet is
Correct Answer: a) 100 Gauss
For a short magnet, the axial field (\( B_{axial} \)) is twice the equatorial field (\( B_{eq} \)) at the same distance.
Given \( B_{axial} = 200 \) Gauss, then \( B_{eq} = \frac{B_{axial}}{2} = 100 \) Gauss.
8. The magnetic moment of an electron revolving in a circular orbit of radius r with speed v is given by
Correct Answer: a) \( \frac{evr}{2} \)
The magnetic moment (\( \mu \)) of a current loop is given by \( \mu = IA \), where \( I \) is the current and \( A \) is the area.
For an electron in orbit, \( I = \frac{e}{T} = \frac{ev}{2\pi r} \) and \( A = \pi r^2 \).
Thus, \( \mu = \frac{ev}{2\pi r} \times \pi r^2 = \frac{evr}{2} \).
9. An iron rod of length L and magnetic moment M is bent in the form of a semicircle. Now its magnetic moment will be
Correct Answer: a) \( \frac{2M}{\pi} \)
When the rod is bent into a semicircle, the effective distance between the poles becomes the diameter (\( d = \frac{2L}{\pi} \)).
The new magnetic moment \( M' = m \times d = m \times \frac{2L}{\pi} \).
Since the original moment \( M = m \times L \), we get \( M' = \frac{2M}{\pi} \).
10. 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 θ is
Correct Answer: a) \( MB(1 - \cosθ) \)
The work done in rotating a magnetic dipole in a magnetic field is given by \( W = MB(1 - \cosθ) \).
This comes from integrating the torque \( \tau = MB\sinθ \) over the angular displacement.
11. 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
Correct Answer: d) \( d^4 \)
When like poles face each other and the magnet length is negligible compared to distance d, the force between two magnetic dipoles is given by \( F \propto \frac{1}{d^4} \).
This is because the field of a dipole falls off as \( 1/d^3 \), and the interaction between two dipoles gives the \( 1/d^4 \) dependence.
12. A bar magnet of magnetic moment 10⁴ J/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
Correct Answer: a) 0.2 J
The work done is given by \( W = MB(1 - \cosθ) \).
Here, \( M = 10^4 \) J/T, \( B = 4 \times 10^{-5} \) T, and \( θ = 60° \).
So, \( W = 10^4 \times 4 \times 10^{-5} \times (1 - \cos60°) = 0.4 \times 0.5 = 0.2 \) J.
13. A long magnet is cut in two parts in such a way that the ratio of their lengths is 2 : 1. The ratio of pole strengths of both the section is
Correct Answer: a) Equal
When a magnet is cut, the pole strength remains the same for all pieces. The magnetic moment changes because it depends on the length (\( M = m \times l \)), but the pole strength \( m \) remains unchanged.
14. Unit of magnetic flux density (or magnetic induction) is
Correct Answer: d) All of the above
Magnetic flux density (B) can be expressed in multiple equivalent units:
Tesla (T) is the SI unit, Weber per square meter (Wb/m²) is another representation,
and Newton per ampere-meter (N/A-m) is also correct as \( 1 T = 1 N/(A \cdot m) \).
15. The magnetic field inside a long solenoid is
Correct Answer: a) Uniform and parallel to the axis
Inside a long solenoid, the magnetic field is nearly uniform and parallel to the axis of the solenoid.
The field strength is given by \( B = \mu_0 nI \), where \( n \) is the number of turns per unit length and \( I \) is the current.
16. A sensitive magnetic instrument can be shielded very effectively from outside magnetic fields by placing it inside a box of
Correct Answer: c) Soft iron of high permeability
Soft iron with high permeability provides excellent magnetic shielding because it conducts magnetic flux lines around the shielded volume,
diverting them away from the interior. This is known as a magnetic shield.
17. The magnetic moment of an atom is due to
Correct Answer: c) Both orbital and spin motion of electrons
The magnetic moment of an atom arises from both the orbital motion of electrons around the nucleus and the intrinsic spin of the electrons.
In most materials, the spin contribution dominates.
18. If the magnetic flux is expressed in weber, then magnetic induction can be expressed in
Correct Answer: a) Weber/m²
Magnetic induction (B) is magnetic flux (Φ) per unit area, so its unit is weber per square meter (Wb/m²),
which is equivalent to the tesla (T), the SI unit of magnetic field strength.
19. A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 60°. The torque required to maintain the needle in this position will be
Correct Answer: c) \( \sqrt{3}W \)
The work done is \( W = MB(1 - \cos60°) = MB(0.5) \), so \( MB = 2W \).
The torque at 60° is \( \tau = MB\sin60° = 2W \times \frac{\sqrt{3}}{2} = \sqrt{3}W \).
20. Force between two unit pole strength placed at a distance of one metre is
Correct Answer: b) \( 10^{-7} \) N
According to Coulomb's law for magnetism, \( F = \frac{\mu_0}{4\pi} \frac{m_1 m_2}{r^2} \).
For unit poles at 1m distance, \( F = \frac{4\pi \times 10^{-7}}{4\pi} \times \frac{1 \times 1}{1^2} = 10^{-7} \) N.
21. The small magnets each of magnetic moment 10 A-m² are placed end-on position 0.1m apart from their centres. The force acting between them is
Correct Answer: c) \( 6 \times 10^{-4} \) N
The force between two magnetic dipoles in end-on position is \( F = \frac{3\mu_0}{2\pi} \frac{M_1 M_2}{r^4} \).
Substituting \( M_1 = M_2 = 10 \) A-m², \( r = 0.1 \) m, and \( \mu_0 = 4\pi \times 10^{-7} \),
we get \( F = \frac{3 \times 4\pi \times 10^{-7}}{2\pi} \times \frac{10 \times 10}{(0.1)^4} = 6 \times 10^{-7} \times 10^3 = 6 \times 10^{-4} \) N.
22. The magnetic susceptibility of a diamagnetic material is
Correct Answer: b) Small and negative
Diamagnetic materials have a small negative magnetic susceptibility (\( -1 \ll \chi < 0 \)).
They are weakly repelled by magnetic fields due to induced magnetic moments opposing the applied field.
23. The Curie temperature is the temperature above which
Correct Answer: b) A ferromagnetic material becomes paramagnetic
The Curie temperature is the critical temperature above which a ferromagnetic material loses its spontaneous magnetization and becomes paramagnetic.
This occurs due to thermal energy disrupting the alignment of magnetic domains.
24. The direction of line of magnetic field of bar magnet is
Correct Answer: d) From south pole to north pole inside the magnet and from north pole to south pole outside the magnet
Magnetic field lines form continuous closed loops. Outside the magnet, they go from north to south pole,
while inside the magnet, they complete the loop by going from south to north pole.
25. Force between two identical bar magnets whose centres are r metre apart is 4.8 N, when their axes are in the same line. If separation is increased to 2r, the force between them is reduced to
Correct Answer: d) 0.3 N
For two identical bar magnets with axes aligned, the force is proportional to \( 1/r^4 \).
When distance increases from r to 2r, the force becomes \( \frac{4.8}{(2)^4} = \frac{4.8}{16} = 0.3 \) N.
26. A magnetic needle is kept in a non-uniform magnetic field. It experiences
Correct Answer: a) A force and a torque
In a non-uniform field, a magnetic dipole experiences both a torque (trying to align it with the field)
and a net force (due to the field gradient causing unequal forces on the two poles).
27. Magnetic lines of force due to a bar magnet do not intersect because
Correct Answer: a) A point always has a single net magnetic field
Magnetic field lines cannot intersect because at any point in space, there can only be one direction and magnitude of the magnetic field.
Intersection would imply two different field directions at the same point, which is physically impossible.
28. The incorrect statement regarding the lines of force of the magnetic field B is
Correct Answer: a) Magnetic intensity is a measure of lines of force passing through unit area held normal to it
Statement (a) is incorrect because magnetic flux density (B), not magnetic intensity (H), is the measure of lines of force per unit area.
Magnetic intensity is related to the magnetizing field and is measured in A/m.
29. There is no couple acting when two bar magnets are placed coaxially separated by a distance because
Correct Answer: d) The forces act along the same line
When magnets are placed coaxially, the forces between their poles act along the same line (the axis),
resulting in no perpendicular distance between forces to create a torque or couple.
30. The magnetic permeability of a ferromagnetic material with increasing applied magnetic field
Correct Answer: c) First increases then decreases
The permeability of ferromagnetic materials first increases as domains align with the field, reaches a maximum,
then decreases as saturation is approached where all domains are aligned and further field increases produce little additional magnetization.
31. A bar magnet of magnetic moment \( \vec{M} \) is placed in a magnetic field of induction \( \vec{B} \). The torque exerted on it is
Correct Answer: a) \( \vec{M} \times \vec{B} \)
The torque (\( \vec{\tau} \)) on a magnetic dipole in a magnetic field is given by the cross product \( \vec{\tau} = \vec{M} \times \vec{B} \).
This torque tends to align the magnetic moment with the field direction.
32. The hysteresis loop for a ferromagnetic material is narrow for
Correct Answer: a) Soft magnetic materials
Soft magnetic materials have a narrow hysteresis loop, indicating low coercivity and low energy loss during magnetization cycles.
Hard magnetic materials have wide hysteresis loops with high coercivity.
33. Magnetic lines of force
Correct Answer: b) Are always closed
Magnetic field lines are continuous and always form closed loops, unlike electric field lines which begin and end on charges.
This reflects the fact that there are no magnetic monopoles.
34. The magnet can be completely demagnetized by
Correct Answer: d) A reverse field of appropriate strength
Complete demagnetization requires applying a reverse magnetic field that cycles with decreasing amplitude (AC demagnetization)
or bringing the material above its Curie temperature. Simply breaking a magnet only creates smaller magnets.
35. The magnetic moment of an electron due to its spin is approximately
Correct Answer: a) \( 9.27 \times 10^{-24} \) A·m²
The spin magnetic moment of an electron is approximately one Bohr magneton (\( \mu_B \)),
which is \( \mu_B = \frac{e\hbar}{2m_e} \approx 9.27 \times 10^{-24} \) A·m².
36. The magnetic field at the center of a current carrying circular loop of radius R is proportional to
Correct Answer: c) \( 1/R \)
The magnetic field at the center of a circular loop is \( B = \frac{\mu_0 I}{2R} \),
where \( I \) is the current and \( R \) is the radius. Thus, \( B \propto 1/R \).
37. Weber/m² is equal to
Correct Answer: c) Tesla
The tesla (T) is the SI unit of magnetic flux density, and 1 T = 1 Wb/m².
While weber (Wb) is the unit of magnetic flux and henry (H) is the unit of inductance,
they are not equivalent to Wb/m².
38. Two like magnetic poles of strength 10 and 40 SI units are separated by a distance 30 cm. The intensity of magnetic field is zero on the line joining them
Correct Answer: a) At a point 10 cm from the stronger pole
For like poles, the neutral point occurs closer to the weaker pole.
Let x be distance from 40 unit pole: \( \frac{40}{x^2} = \frac{10}{(0.3-x)^2} \).
Solving gives \( x = 0.2 \) m (20 cm from 40 pole, or 10 cm from 10 pole).
The answer is 10 cm from the stronger (40 unit) pole.
39. The intensity of magnetic field is H and moment of magnet is M. The maximum potential energy is
Correct Answer: a) MH
The potential energy of a magnetic dipole in a field is \( U = -\vec{M} \cdot \vec{H} = -MH\cosθ \).
The maximum potential energy occurs when θ = 180° (anti-parallel), giving \( U_{max} = MH \).
40. The relative permeability of a superconductor is
Correct Answer: a) Zero
Superconductors exhibit perfect diamagnetism (Meissner effect), with relative permeability \( \mu_r = 0 \).
They expel all magnetic flux from their interior when cooled below their critical temperature.
41. A magnet of magnetic moment \( 25\hat{i} \) A·m² is placed along the x-axis in a magnetic field \( (3\hat{i} + 4\hat{j}) \) T. The torque acting on the magnet is
Correct Answer: d) \( 100\hat{k} \) N·m
Torque \( \vec{\tau} = \vec{M} \times \vec{B} = 25\hat{i} \times (3\hat{i} + 4\hat{j}) = 25 \times 4 (\hat{i} \times \hat{j}) = 100\hat{k} \) N·m.
The \( \hat{i} \times \hat{i} \) term is zero.
42. The effective length of a magnet is 31.4 cm and its pole strength is 0.5 Am. The magnetic moment, if it is bent in the form of a semicircle will be
Correct Answer: a) 0.1 A·m²
When bent into a semicircle, the effective distance between poles becomes the diameter.
For circumference \( \pi r = 0.314 \) m, radius \( r = 0.1 \) m, so diameter = 0.2 m.
Magnetic moment \( M = m \times d = 0.5 \times 0.2 = 0.1 \) A·m².
43. A bar magnet of magnetic moment 3.0 A·m² is placed in a uniform magnetic induction field of 2 × 10⁻⁵ T. If each pole of the magnet experiences a force of 6 × 10⁻⁴ N, the length of the magnet is
Correct Answer: d) 0.1 m
Force on each pole \( F = mB \). Total moment \( M = m \times l \).
Combining: \( l = \frac{M}{m} = \frac{M}{F/B} = \frac{MB}{F} = \frac{3 \times 2 \times 10^{-5}}{6 \times 10^{-4}} = \frac{6 \times 10^{-5}}{6 \times 10^{-4}} = 0.1 \) m.
44. Two lines of force due to a bar magnet
Correct Answer: d) Do not intersect at all
Magnetic field lines never intersect because that would imply two different directions of the magnetic field at a single point,
which is physically impossible. They form continuous, non-intersecting loops.
45. The magnetic field inside a toroid is
Correct Answer: d) Circular and concentric with the toroid
Inside a toroid, the magnetic field forms circular loops that are concentric with the toroid's circular axis.
The field strength varies inversely with the distance from the center of the toroid.
46. The ultimate individual unit of magnetism in any magnet is called
Correct Answer: c) Dipole
The smallest unit of magnetism is the magnetic dipole, which consists of a north and south pole that cannot be separated.
All magnetic phenomena can be explained in terms of dipoles, as isolated magnetic monopoles do not exist.
47. The magnetic lines of force inside a bar magnet
Correct Answer: a) Are from south-pole to north-pole of the magnet
Magnetic field lines form continuous closed loops. Inside the magnet, they run from the south pole to the north pole,
completing the loop that runs from north to south outside the magnet.
48. The magnetic susceptibility of a ferromagnetic material is
Correct Answer: c) Large and positive
Ferromagnetic materials have a large positive magnetic susceptibility (\( \chi \gg 1 \)) due to the alignment of magnetic domains.
They are strongly attracted to magnetic fields and can retain magnetization.
49. The work done in rotating a magnet of magnetic moment 2 A·m² in a magnetic field of 5 × 10⁻³ T from the direction along the magnetic field to opposite direction to the magnetic field, is
Correct Answer: b) 2 × 10⁻² J
Work done \( W = MB(1 - \cosθ) \). From θ = 0° to 180°, \( W = 2 \times 5 \times 10^{-3} (1 - (-1)) = 10^{-2} \times 2 = 2 \times 10^{-2} \) J.
50. A magnet of magnetic moment 10 A·m² is aligned in the direction of magnetic field of 0.1 T. What is the net work done to bring the magnet normal to the magnetic field
Correct Answer: c) 1 J
Work done \( W = MB(1 - \cosθ) \). From θ = 0° to 90°, \( W = 10 \times 0.1 (1 - 0) = 1 \) J.