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

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

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A class 12 student is performing an experiment with a bar magnet and iron filings sprinkled on a glass sheet placed over it. She observes that the iron filings arrange themselves in a characteristic pattern around the magnet, forming curved paths that emerge from one end and curve around to enter the other end. Her teacher explains that this pattern represents the magnetic field lines of the bar magnet and that a similar pattern is seen around a current-carrying solenoid. The teacher further points out that these field lines have specific properties that distinguish them from electric field lines of an electric dipole, and that understanding these properties is fundamental to the study of magnetism.

Question 1: State any two properties of magnetic field lines as observed in the iron filing experiment.

Magnetic field lines form continuous closed loops, emerging from one end (north pole) and entering the other end (south pole), completing the loop inside the magnet.
Magnetic field lines never intersect each other; if they did, the direction of the net magnetic field at the point of intersection would be ambiguous.

Question 2: How does the density of iron filings in the pattern relate to the magnitude of the magnetic field B at that region?

The larger the number of field lines crossing per unit area, the stronger is the magnitude of the magnetic field B at that region.
In the iron filing pattern, filings are more densely packed near the poles (ends) of the bar magnet, indicating the field is stronger there than in the middle region.

Question 3: The teacher states that the bar magnet pattern is similar to that of a current-carrying solenoid. Explain this analogy and state what happens when the bar magnet is cut into two halves transverse to its length.

A bar magnet can be thought of as a large number of circulating currents in analogy with a solenoid; both produce nearly identical external magnetic field patterns as confirmed by iron filing arrangements and compass needle deflections.
The axial field of a finite solenoid at large distances is B = (mu0/4pi)(2m/r^3), which is identical to the far axial field formula of a bar magnet, making the analogy mathematically firm.
When a bar magnet is cut into two halves transverse to its length, each piece becomes a complete smaller bar magnet with its own north pole and south pole — analogous to cutting a solenoid into two smaller solenoids, each with weaker but complete magnetic properties.

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Case Set 2

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During a science exhibition, a student demonstrates the Meissner effect by cooling a small ceramic disk to liquid nitrogen temperature and placing a permanent magnet above it. To the audience's amazement, the magnet floats stably above the disk without any mechanical support. The student explains that the disk has become a superconductor at low temperatures, exhibiting a special magnetic property not seen in ordinary diamagnetic materials like bismuth or copper. The physics teacher present explains that this property is quantified by specific values of magnetic susceptibility and relative magnetic permeability, and has potential applications in transportation technology.

Question 1: Identify the magnetic property demonstrated and state the values of chi and mu_r for the superconducting disk.

The phenomenon demonstrated is perfect diamagnetism, called the Meissner effect, observed in superconductors cooled to very low temperatures.
For a superconductor, chi = -1 and mu_r = 0, meaning the external magnetic field is completely expelled from the interior of the material.

Question 2: How does this demonstration differ from the behaviour of an ordinary diamagnetic material like bismuth placed near a magnet?

Ordinary diamagnetic materials like bismuth have a small negative susceptibility (chi approximately -10^-5); they are only weakly repelled by a magnet and the reduction in field inside is about one part in 10^5.
A superconductor has chi = -1 (perfect diamagnet), completely expelling the field; the repulsion is strong enough to levitate a magnet, which is impossible with ordinary diamagnets like bismuth.

Question 3: Explain the mechanism of ordinary diamagnetism at the atomic level and state why diamagnetism is said to be universal yet rarely the dominant magnetic property observed.

Electrons orbiting atomic nuclei possess orbital magnetic moments; when an external field is applied, electrons with moments along the field slow down and those opposing it speed up, in accordance with Lenz's law, inducing a net moment opposing the applied field.
This induced opposing moment causes repulsion — diamagnetism — and is present in all atoms because all atoms have orbiting electrons.
Diamagnetism is universal but extremely weak (field reduction of about 1 part in 10^5); in materials that also have paramagnetic or ferromagnetic properties, these stronger effects dominate and mask the diamagnetic contribution.

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Case Set 3

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A physics teacher sets up a demonstration to explain Gauss's law for magnetism. She draws two closed Gaussian surfaces around a bar magnet — one small surface enclosing only the north pole region and one large surface enclosing the entire magnet. Students are asked to count (estimate from the diagram) the number of field lines entering and leaving each surface. In the first surface (enclosing only the north pole), some lines seem to leave through the top, but the teacher points out that field lines also enter through the sides and bottom because the lines curve around and re-enter. She then compares this with Gauss's law for electrostatics where a surface enclosing a positive charge gives a net outward flux.

Question 1: State Gauss's law for magnetism in mathematical form and explain what phi_B = 0 implies physically.

Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero: phi_B = sum (all area elements) B.Delta_S = 0.
Physically, this means there are no sources or sinks of magnetic field B; magnetic field lines are continuous closed loops with no beginning or end, and for every field line leaving a closed surface, another must enter it.

Question 2: How does Gauss's law for magnetism differ from Gauss's law for electrostatics? What fundamental difference in nature is responsible?

In electrostatics, Gauss's law gives sum E.Delta_S = q/epsilon0; the flux through a closed surface equals the enclosed charge divided by epsilon0, which can be non-zero.
In magnetism, the corresponding law gives sum B.Delta_S = 0 always; the difference arises because isolated magnetic poles (monopoles) do not exist, unlike isolated electric charges.

Question 3: If magnetic monopoles were discovered, how would Gauss's law for magnetism be modified? Describe the impact on the nature of magnetic field lines.

If magnetic monopoles of magnetic charge q_m existed, Gauss's law for magnetism would be modified to: the integral of B.dS over a closed surface equals mu0 * q_m, analogous to Gauss's law for electrostatics.
Magnetic field lines would no longer always be continuous closed loops; they could originate from a north monopole (source) and terminate on a south monopole (sink), just as electric field lines start on positive and end on negative charges.
The fundamental asymmetry between electric and magnetic phenomena — isolated electric charges exist but magnetic monopoles do not — would disappear, and Maxwell's equations would become fully symmetric between electric and magnetic fields.

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Case Set 4

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A research engineer is designing an electromagnet for an industrial application. She has access to three core materials: material X with chi = -0.00001, material Y with chi = +0.00002, and material Z with chi = 1500. She winds a solenoid of 1000 turns per metre, passes a current of 2 A, and measures the resultant field with each core. With material X, the field is slightly reduced; with material Y, it is slightly enhanced; with material Z, the field is enormously amplified. She notes that for material Z, the individual atomic dipoles spontaneously align within macroscopic regions even without an external field, a phenomenon that requires quantum mechanical explanation.

Question 1: Identify the type of magnetic material for each of X, Y, and Z based on their susceptibility values.

Material X with chi = -0.00001 is diamagnetic (chi is small and negative); material Y with chi = +0.00002 is paramagnetic (chi is small and positive).
Material Z with chi = 1500 is ferromagnetic (chi is very large and positive, chi >> 1).

Question 2: Calculate the relative magnetic permeability mu_r for material Z and state how it affects the magnetic field inside the solenoid compared to an air-core solenoid.

Relative magnetic permeability for material Z: mu_r = 1 + chi = 1 + 1500 = 1501.
The magnetic field inside the solenoid with material Z is B = mu_r * mu0 * H = 1501 times greater than B0 = mu0 * H for an air-core solenoid carrying the same current, demonstrating the enormous field amplification by ferromagnetic cores.

Question 3: Explain the domain theory that accounts for the behaviour of material Z. What happens to the domain structure when the external field is removed, and how does this distinguish hard from soft ferromagnets?

In material Z (ferromagnetic), quantum mechanical exchange forces cause atomic dipoles to spontaneously align within macroscopic regions called domains (typically 1 mm, ~10^11 atoms); each domain has a net magnetisation but initially domains are randomly oriented giving no bulk magnetisation.
On applying external field B0, domains oriented along B0 grow at the expense of others; eventually a single giant aligned domain forms, producing very strong net magnetisation — the field lines become highly concentrated inside the material.
Hard ferromagnets (e.g., Alnico) retain domain alignment after field removal and form permanent magnets; soft ferromagnets (e.g., soft iron) have domains that revert to random orientation when the field is removed, making them suitable for temporary electromagnets.

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Case Set 5

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In a thought experiment, a student imagines placing a small magnetised compass needle of known magnetic moment m at various positions around a bar magnet. At position P (on the axis), the compass needle aligns along the axis. At position Q (on the equatorial line), it aligns perpendicular to the axis. The student then calculates the potential energy of the needle in each configuration using U = -m.B and tries to determine which configuration is most stable and which is most unstable. The teacher explains that the torque formula tau = m x B and the potential energy formula U = -m.B together completely describe the behaviour of a dipole in an external field.

Question 1: Write the expressions for the axial field BA and equatorial field BE of a short bar magnet of moment m at distance r. State the ratio BA/BE.

Axial field: BA = (mu0/4pi)(2m/r^3), directed along m (the direction of the magnetic moment).
Equatorial field: BE = -(mu0/4pi)(m/r^3), directed opposite to m; the ratio BA/BE = 2 in magnitude, meaning the axial field is twice the equatorial field at the same distance.

Question 2: A compass needle of magnetic moment m is placed on the axial line of the bar magnet with its moment parallel to BA. What is its potential energy and what type of equilibrium does it represent?

When m is parallel to BA (theta = 0 degrees), the potential energy is U = -m.B = -mBA (minimum value), representing the most stable equilibrium.
In this configuration the torque tau = mBA sin(0) = 0; any small perturbation results in a restoring torque that brings the needle back to this alignment, confirming stable equilibrium.

Question 3: Using the electrostatic analogy, explain how the magnetic dipole equations are derived from electric dipole equations. Write at least three corresponding pairs from the dipole analogy table.

The electrostatic analogy states that magnetic dipole equations are obtained from electric dipole equations by substituting: E with B, dipole moment p with m, and the factor 1/(4pi*epsilon0) with mu0/(4pi).
First pair: equatorial field of electric dipole -p/(4pi*epsilon0*r^3) maps to equatorial field of magnetic dipole -mu0*m/(4pi*r^3).
Second pair: torque on electric dipole p x E maps to torque on magnetic dipole m x B; third pair: potential energy -p.E maps to magnetic potential energy -m.B — giving a complete mathematical correspondence for all dipole interactions in external fields.

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Chapter 5: Magnetism and Matter | Case Study Questions

Passage

Question 1: State any two properties of magnetic field lines as observed in the iron filing experiment.

Question 2: How does the density of iron filings in the pattern relate to the magnitude of the magnetic field B at that region?

Question 3: The teacher states that the bar magnet pattern is similar to that of a current-carrying solenoid. Explain this analogy and state what happens when the bar magnet is cut into two halves transverse to its length.

Passage

Question 1: Identify the magnetic property demonstrated and state the values of chi and mu_r for the superconducting disk.

Question 2: How does this demonstration differ from the behaviour of an ordinary diamagnetic material like bismuth placed near a magnet?

Question 3: Explain the mechanism of ordinary diamagnetism at the atomic level and state why diamagnetism is said to be universal yet rarely the dominant magnetic property observed.

Passage

Question 1: State Gauss's law for magnetism in mathematical form and explain what phi_B = 0 implies physically.

Question 2: How does Gauss's law for magnetism differ from Gauss's law for electrostatics? What fundamental difference in nature is responsible?

Question 3: If magnetic monopoles were discovered, how would Gauss's law for magnetism be modified? Describe the impact on the nature of magnetic field lines.

Passage

Question 1: Identify the type of magnetic material for each of X, Y, and Z based on their susceptibility values.

Question 2: Calculate the relative magnetic permeability mu_r for material Z and state how it affects the magnetic field inside the solenoid compared to an air-core solenoid.

Question 3: Explain the domain theory that accounts for the behaviour of material Z. What happens to the domain structure when the external field is removed, and how does this distinguish hard from soft ferromagnets?

Passage

Question 1: Write the expressions for the axial field BA and equatorial field BE of a short bar magnet of moment m at distance r. State the ratio BA/BE.

Question 2: A compass needle of magnetic moment m is placed on the axial line of the bar magnet with its moment parallel to BA. What is its potential energy and what type of equilibrium does it represent?

Question 3: Using the electrostatic analogy, explain how the magnetic dipole equations are derived from electric dipole equations. Write at least three corresponding pairs from the dipole analogy table.

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