Chapter 5: Magnetism and Matter Long Questions | physics Class 12 CBSE

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Chapter 5: Magnetism and Matter Long Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Compare the properties of magnetic field lines of a bar magnet with those of electric field lines of an electric dipole, highlighting both similarities and differences.

Both bar magnet and electric dipole field lines have similar patterns at large distances; the axial and equatorial field expressions are mathematically analogous.
Electric field lines originate from positive charges and terminate on negative charges or go to infinity, whereas magnetic field lines form continuous closed loops with no starting or ending points.
The density of field lines represents field strength in both cases; a tangent to any field line gives the field direction; neither set of field lines crosses itself.
The analogy breaks down fundamentally: isolated magnetic poles do not exist, so magnetic field lines have no sources or sinks, while electric dipole lines do have source charges.
Magnetic field lines do not indicate the direction of force on a moving charge (force = qv x B is perpendicular to B), whereas electric field lines do show the force direction on a positive charge.

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Question 2

Long Form

Derive the expression for torque and potential energy of a magnetic dipole placed in a uniform magnetic field and discuss the equilibrium positions.

A magnetic dipole of moment m in field B experiences equal and opposite forces on its poles, giving zero net force but a torque tau = m x B; in magnitude tau = mB sin(theta).
The potential energy is obtained by integrating the torque: U = integral(tau d_theta) = -mB cos(theta) = -m.B, with zero chosen at theta = 90 degrees.
At theta = 0 degrees (m parallel to B), U = -mB is minimum; this is the most stable equilibrium position with zero torque.
At theta = 180 degrees (m antiparallel to B), U = +mB is maximum; this is the most unstable equilibrium — zero torque but any perturbation causes rotation.
At theta = 90 degrees, U = 0 and torque is maximum (mB); the dipole is not in equilibrium here.

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Question 3

Long Form

Explain the analogy between a bar magnet and a current-carrying solenoid. How does cutting each in half lead to similar outcomes?

A bar magnet can be modelled as a collection of circulating currents, analogous to a solenoid, since both produce nearly identical external field patterns, including similar iron filing arrangements.
The axial field of a finite solenoid at large distances is B = (mu0/4pi)(2m/r^3), which matches the far axial field formula of a bar magnet, confirming the analogy.
Cutting a bar magnet in half (transverse to its length) is like cutting a solenoid; each half becomes a complete smaller magnet with a north pole and a south pole, with somewhat weaker properties.
The field lines in both the bar magnet and solenoid pieces remain continuous — emerging from one face and entering the other — there are no isolated poles.
The analogy can be verified experimentally by moving a compass needle near both a bar magnet and a current-carrying solenoid and observing similar deflections.

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Question 4

Long Form

State and explain Gauss's law for magnetism. How does it lead to the conclusion that magnetic monopoles do not exist?

Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero: phi_B = sum B.Delta_S = 0, for all closed surfaces.
Magnetic field lines are continuous and form closed loops; the number entering any closed Gaussian surface always equals the number leaving it.
In electrostatics, Gauss's law gives sum E.Delta_S = q/epsilon0, which is non-zero when charge q is enclosed; this reflects the existence of isolated charges (monopoles for charge).
If magnetic monopoles existed, Gauss's law for magnetism would be modified: the right-hand side would equal mu0 * q_m, where q_m is the magnetic charge enclosed — analogous to Gauss's law for electrostatics.
Since no such non-zero flux is ever observed, there are no sources or sinks of B, confirming that magnetic monopoles do not exist; the simplest magnetic element is a dipole or current loop.

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Question 5

Long Form

Define magnetisation M, magnetic intensity H, and magnetic susceptibility chi. Write the relation connecting B, H, and M and explain how chi distinguishes diamagnetic from paramagnetic materials.

Magnetisation M = m_net/V is the net magnetic moment per unit volume; it represents the material's contribution to the total magnetic field and is measured in A/m.
Magnetic intensity H = B/mu0 - M represents the contribution of external currents (e.g., in a solenoid) to B, independent of the material; also in A/m.
The total field is B = mu0(H + M); the material's response is M = chi*H, where chi (dimensionless) is the magnetic susceptibility.
For diamagnetic materials chi is small and negative (approx -10^-5): M opposes H, the material is weakly repelled, and field lines are expelled.
For paramagnetic materials chi is small and positive (approx +10^-5): M is along H, the material is weakly attracted, and field lines concentrate inside — a tiny difference in chi produces radically different macroscopic behaviour.

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Question 6

Long Form

Describe the origin of diamagnetism at the atomic level and explain why superconductors are considered perfect diamagnets.

Electrons orbiting atomic nuclei possess orbital angular momentum and act as current loops with an orbital magnetic moment; diamagnetism arises from the response of these orbital moments to an applied field.
When an external field is applied, electrons whose orbital moments are along the field slow down, and those opposed speed up, in accordance with Lenz's law; the net induced moment opposes the applied field, producing repulsion.
Diamagnetism is universal — present in all materials — but it is very weak (reduction of field by about 1 part in 10^5) and is masked by paramagnetism or ferromagnetism in most materials.
In superconductors (metals at very low temperatures), the diamagnetic effect is perfect: chi = -1 and mu_r = 0; the external field is completely expelled from the interior.
This perfect diamagnetism is called the Meissner effect; a superconductor repels a magnet by Newton's third law, enabling applications like magnetically levitated superfast trains.

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Question 7

Long Form

Compare diamagnetic, paramagnetic, and ferromagnetic materials in terms of susceptibility, relative permeability, behaviour in external field, and examples.

Diamagnetic: chi ranges from -1 to 0 (small negative); mu_r between 0 and 1 (less than 1); material moves from strong to weak field; field lines are expelled. Examples: bismuth, copper, water.
Paramagnetic: chi is small and positive (0 < chi < epsilon); mu_r slightly greater than 1; material moves from weak to strong field; field lines concentrate inside. Examples: aluminium, oxygen, sodium.
Ferromagnetic: chi >> 1 (very large positive); mu_r >> 1 (can exceed 1000); material is strongly attracted to magnets; field lines are highly concentrated inside. Examples: iron, cobalt, nickel, gadolinium.
For paramagnetic and ferromagnetic materials, chi and mu_r depend on temperature; above the Curie temperature, ferromagnets become paramagnetic.
A minuscule difference in chi (e.g., -10^-5 versus +10^-5) produces radically opposite macroscopic behaviours — repulsion versus attraction — illustrating the sensitivity of magnetic classification.

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Question 8

Long Form

Describe the domain theory of ferromagnetism. How does an external magnetic field change the domain structure, and what distinguishes hard from soft ferromagnets?

Ferromagnetic atoms possess magnetic dipole moments that interact via quantum mechanical exchange forces, causing spontaneous alignment in macroscopic regions called domains (~1 mm, ~10^11 atoms each).
Without an external field, different domains are randomly oriented, so there is no bulk magnetisation; this is represented schematically in Fig. 5.8(a).
On applying an external field B0, domains oriented along B0 grow in size at the expense of unfavourably oriented domains, and eventually a single 'giant' aligned domain forms, producing strong net magnetisation.
Hard ferromagnets (e.g., Alnico, lodestone) retain magnetisation after field removal due to strong domain pinning; they are used for permanent magnets and compass needles.
Soft ferromagnets (e.g., soft iron) lose magnetisation when the field is removed because domain walls move easily; they are used where switching magnetisation quickly is needed.

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Long Answer

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Hard

Question 9

Long Form

Starting from the field due to a bar magnet of moment m, write and compare the axial and equatorial field expressions. Show how these follow from the electrostatic analogy.

For a bar magnet of moment m at a distance r >> l (l = half-length), the axial field is BA = (mu0/4pi)(2m/r^3) directed along m; the equatorial field is BE = -(mu0/4pi)(m/r^3) directed opposite to m.
The axial field is twice the equatorial field in magnitude at the same distance, and they point in opposite directions.
The electrostatic analogy requires the substitutions: E to B, p to m, and 1/(4pi*epsilon0) to mu0/(4pi); applying these to the electric dipole field formulas directly yields the magnetic expressions above.
This analogy is valid at large distances (r >> l) and confirms that a bar magnet behaves as a magnetic dipole at such distances.
The analogy also extends to torque (p x E maps to m x B) and potential energy (-p.E maps to -m.B), forming a complete correspondence between electric and magnetic dipole physics.

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Question 10

Long Form

Explain the mechanism of paramagnetism. How does an external magnetic field and temperature together influence the magnetisation of a paramagnetic material?

Individual atoms of paramagnetic materials possess permanent magnetic dipole moments due to unpaired electrons; however, ceaseless random thermal motion keeps them disordered, so net magnetisation is zero in the absence of an external field.
On applying an external field B0 at low temperatures, individual dipoles tend to align with B0; the field lines concentrate inside the material and the internal field is enhanced by about 1 part in 10^5.
As field strength increases or temperature decreases, more dipoles align with B0, increasing magnetisation; at very high fields and very low temperatures, all dipoles align — this is the saturation magnetisation.
Both chi and mu_r of a paramagnetic material depend on the material and the sample temperature; lowering temperature increases chi (Curie's law behaviour).
When a paramagnetic bar is placed in a non-uniform field, it tends to move from the region of weak field to the region of strong field — the opposite behaviour from a diamagnetic material.

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Chapter 5: Magnetism and Matter | Long Questions

Compare the properties of magnetic field lines of a bar magnet with those of electric field lines of an electric dipole, highlighting both similarities and differences.

Derive the expression for torque and potential energy of a magnetic dipole placed in a uniform magnetic field and discuss the equilibrium positions.

Explain the analogy between a bar magnet and a current-carrying solenoid. How does cutting each in half lead to similar outcomes?

State and explain Gauss's law for magnetism. How does it lead to the conclusion that magnetic monopoles do not exist?

Define magnetisation M, magnetic intensity H, and magnetic susceptibility chi. Write the relation connecting B, H, and M and explain how chi distinguishes diamagnetic from paramagnetic materials.

Describe the origin of diamagnetism at the atomic level and explain why superconductors are considered perfect diamagnets.

Compare diamagnetic, paramagnetic, and ferromagnetic materials in terms of susceptibility, relative permeability, behaviour in external field, and examples.

Describe the domain theory of ferromagnetism. How does an external magnetic field change the domain structure, and what distinguishes hard from soft ferromagnets?

Starting from the field due to a bar magnet of moment m, write and compare the axial and equatorial field expressions. Show how these follow from the electrostatic analogy.

Explain the mechanism of paramagnetism. How does an external magnetic field and temperature together influence the magnetisation of a paramagnetic material?

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