Magnetism and Matter — Class 12 Physics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 12 Physics chapter "Magnetism and Matter" — 6 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 12 Physics chapter "Magnetism and Matter" — 6 important questions with detailed answers for CBSE board exa…
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NCERT Solutions for Class 12 Physics — Magnetism and Matter. Step-by-step answers to all 6 textbook questions from this chapter, written for CBSE board preparation and free to use.
Magnetism and Matter — All 6 Questions Solved
Q1. Define magnetic susceptibility. Write its relation with relative permeability.
Magnetic Susceptibility (χ_m - chi): Measure of ease with which material gets magnetized.
χ_m = M/H
where M = magnetization (magnetic moment per unit volume)
H = magnetic field intensity
Dimensionless quantity (no units)
Relation with Relative Permeability:
μᵣ = 1 + χ_m
where μᵣ = relative permeability
Alternative:
B = μ₀(H + M) = μ₀(1 + χ_m)H = μ₀μᵣH
Classification of Materials:
1. Diamagnetic: χ_m < 0 (small negative)
μᵣ < 1 (slightly less than 1)
Examples: Copper, bismuth, water
2. Paramagnetic: χ_m > 0 (small positive)
μᵣ > 1 (slightly greater than 1)
Examples: Aluminum, manganese
3. Ferromagnetic: χ_m >> 0 (very large positive)
μᵣ >> 1 (much greater than 1)
Examples: Iron, nickel, cobalt
Show permanent magnetization and hysteresis
Temperature dependence:
- Paramagnetic and ferromagnetic susceptibilities decrease with temperature
- Diamagnetic susceptibility nearly independent of temperature
Q2. What is magnetic permeability? Distinguish between μ, μ₀, and μᵣ.
Magnetic Permeability (μ): Ability of material to support magnetic field.
μ = B/H
where B = magnetic flux density
H = magnetic field intensity
SI Unit: Henry per meter (H/m) or T⋅m/A
Alternatively: T⋅m/A or Wb/(A⋅m)
Three types:
1. Absolute Permeability (μ):
μ = B/H
Dimension: [H/m] or [T⋅m/A]
Value depends on material
Used in material science
2. Permeability of Free Space (μ₀):
μ₀ = 4π × 10⁻⁷ H/m = 4π × 10⁻⁷ T⋅m/A
Constant for vacuum and air
Fundamental constant in electromagnetism
3. Relative Permeability (μᵣ):
μᵣ = μ/μ₀ = B/(μ₀H)
Dimensionless quantity
Characteristic of material
μᵣ = 1 + χ_m
Relations:
μ = μᵣμ₀
B = μH = μᵣμ₀H = μ₀(H + M)
Typical values of μᵣ:
- Vacuum: μᵣ = 1 (by definition)
- Air: μᵣ ≈ 1.0000004
- Copper: μᵣ ≈ 0.999991 (diamagnetic)
- Aluminum: μᵣ ≈ 1.000023 (paramagnetic)
- Iron: μᵣ ≈ 4000-6000 (ferromagnetic)
- μ-metal: μᵣ ≈ 100000 (soft ferromagnetic)
Q3. What are diamagnetic materials? Explain diamagnetism from electronic structure viewpoint.
Diamagnetic Materials: Materials that are weakly repelled by magnetic field.
Characteristics:
- Magnetic susceptibility χ_m < 0 (negative)
- Relative permeability μᵣ < 1 (slightly less than 1)
- |χ_m| very small (typically 10⁻⁵ to 10⁻⁶)
- No permanent magnetic moment
- Induced magnetization opposes applied field
Examples: Cu, Bi, Sb, Pb, Si, H₂O, N₂, noble gases
Electronic Structure Explanation:
Origin: Lenz's Law applied to electron motion
Step 1: In atoms, electrons orbit nucleus in closed paths
Step 2: Magnetic field induces change in electron motion
Step 3: By Lenz's law, induced change opposes the change in field
Step 4: Orbital angular momentum L changes, creating induced magnetic moment opposite to field
Induce dipole moment: Δm = -(e²r²)/(4m_e) × B
Step 5: For paired electrons, orbital and spin moments cancel
Step 6: Net induced moment opposes field → diamagnetic
Landor diamagnetic susceptibility:
χ_m = -(Ne²r²)/(6m_e kT) (classical approximation)
Key Points:
- Effect in all materials (due to closed electron orbits)
- Masked by paramagnetism in materials with unpaired electrons
- Independent of temperature (no thermal randomization)
- Only observable in materials WITHOUT unpaired electrons
Practical use: Diamagnetic levitation (superconductors with χ_m = -1)
Q4. What are paramagnetic materials? Explain paramagnetism with examples.
Paramagnetic Materials: Materials weakly attracted to magnetic field.
Characteristics:
- Magnetic susceptibility χ_m > 0 (positive)
- Relative permeability μᵣ > 1 (slightly greater than 1)
- χ_m small (typically 10⁻³ to 10⁻⁵)
- Unpaired electrons in atoms
- Permanent atomic magnetic moments
- Moments randomly oriented → net moment is zero
- Applied field aligns moments → net magnetization
- Loses magnetism when field removed
Examples: Al, Mn, Fe³⁺, Cu²⁺, O₂, paramagnetic salts
Physical Mechanism:
Step 1: Atoms have unpaired electrons
Step 2: Each unpaired electron has spin and orbital angular momentum
Step 3: Resultant creates permanent atomic magnetic dipole moment
Step 4: In absence of field, moments randomly oriented → net moment = 0
Step 5: Applied field exerts torque: τ = m × B
Step 6: Field tends to align moments parallel to itself
Step 7: Thermal energy opposes alignment
Step 8: Result: Partial alignment, net magnetization in field direction
Curie's Law (at moderate temperatures):
χ_m = C/T
where C = Curie constant
T = absolute temperature
Key Points:
- Magnetization proportional to applied field
- Susceptibility decreases with temperature (thermal randomization opposes alignment)
- Magnetization disappears when field removed
- Linear B-H relationship
- No hysteresis
- Paramagnetic effects masked by ferromagnetism if present
Q5. What are ferromagnetic materials? Define and explain ferromagnetism.
Ferromagnetic Materials: Materials strongly attracted to magnetic field and retain magnetization.
Characteristics:
- Very large positive susceptibility χ_m >> 1 (up to 10⁵)
- μᵣ >> 1 (up to 10⁶)
- Permanent strong magnetization
- Retain magnetism after field removal (remnant magnetism)
- Show hysteresis loop
- Magnetization saturates at high fields
- Lose ferromagnetism above Curie temperature T_c
Examples: Fe, Co, Ni, Fe₃O₄, permanent magnets
Explanation:
Exchange Interaction: Quantum mechanical effect
- Electron spins in neighboring atoms interact
- Energy is lowered when spins align parallel
- Creates internal "molecular field" much larger than external field
- Spontaneous alignment of atomic moments
Domain Structure:
Step 1: Ferromagnetic material contains regions called domains
Step 2: Within each domain, atomic moments aligned parallel
Step 3: Domains point in random directions → net moment = 0
Step 4: Domain size: 10⁻⁴ to 10⁻⁶ m
Magnetization Process:
Step 1: Applied field exerts torque on domains
Step 2: Domains with moments parallel to field grow
Step 3: Domains antiparallel to field shrink
Step 4: At saturation, all moments aligned
Hysteresis Curve: B vs H shows path-dependent behavior
- Remnant magnetization (B_r): Field remaining when H = 0
- Coercivity (H_c): Field needed to reduce B to 0
- Saturation (B_s): Maximum field achievable
Curie Temperature (T_c):
- Above T_c: Ferromagnet becomes paramagnetic
- Thermal energy overcomes exchange interaction
- Examples: Fe (770 K), Ni (630 K), Co (1115 K)
Q6. Define magnetic field intensity (H) and magnetization (M). Write relation between B, H, and M.
Magnetic Field Intensity (H):
H = B/μ₀ - M
Alternatively: H = (B - μ₀M)/μ₀
SI Unit: A/m (Ampere per meter)
Dimension: [A/m] or [A·m⁻¹]
Physical meaning:
- Due to free currents only (excluding magnetization currents)
- Independent of material properties
- Measure of applied magnetic field
Magnetization (M):
M = Σm/V (total magnetic dipole moment per unit volume)
SI Unit: A/m (same as H)
Dimension: [A/m]
Physical meaning:
- Magnetic dipole moment density
- Measure of material's magnetic response
- Due to atomic/molecular magnetic moments
- Depends on material and applied field
Relation between B, H, and M:
B = μ₀(H + M)
or B = μ₀H + μ₀M
where μ₀M = magnetization contribution
Using susceptibility χ_m = M/H:
M = χ_m H
B = μ₀(H + χ_m H) = μ₀(1 + χ_m)H = μ₀μᵣH
Alternative expressions:
B = μ₀H + B_m (where B_m = μ₀M is magnetization field)
B = μH (absolute form, where μ = μᵣμ₀)
Comparison with electricity:
- H is analogous to E (electric field intensity)
- M is analogous to P (electric polarization)
- B is analogous to D (electric displacement)
- χ_m is analogous to χ_e (electric susceptibility)
Magnetism and Matter — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. Gauss's Law for magnetism states that:
- A. ∮ E ⋅ dA = Q/ε₀
- B. ∮ B ⋅ dA = 0
- C. ∮ B ⋅ dl = μ₀I
- D. ∮ E ⋅ dl = -dΦB/dt
Answer: B. ∮ B ⋅ dA = 0 — Gauss's Law for magnetism states that the net magnetic flux through any closed surface is always zero, implying that isolated magnetic poles do not exist.
MCQ 2. At a certain place, the horizontal component of Earth's magnetic field is B_H and the total magnetic field is B. If the angle of dip is δ, then:
- A. B_H = B sinδ
- B. B = B_H tanδ
- C. B_H = B cosδ
- D. B = B_H cotδ
Answer: C. B_H = B cosδ — The horizontal component of the Earth's magnetic field (B_H) is related to the total magnetic field (B) and the angle of dip (δ) by the relation B_H = B cosδ.
MCQ 3. A magnetic dipole of magnetic moment M is placed in a uniform magnetic field B. The torque acting on it is given by:
- A. τ = M ⋅ B
- B. τ = M × B
- C. τ = B × M
- D. τ = M/B
Answer: B. τ = M × B — The torque experienced by a magnetic dipole in a uniform magnetic field is given by the cross product of the magnetic moment vector and the magnetic field vector, τ = M × B.
MCQ 4. Which of the following materials is characterized by a negative magnetic susceptibility (χ)?
- A. Paramagnetic
- B. Ferromagnetic
- C. Diamagnetic
- D. Ferrimagnetic
Answer: C. Diamagnetic — Diamagnetic materials are weakly repelled by magnetic fields and have a small, negative magnetic susceptibility, indicating that they develop a magnetization opposite to the applied field.
MCQ 5. Above the Curie temperature, a ferromagnetic material behaves like a:
- A. Diamagnetic material
- B. Paramagnetic material
- C. Another ferromagnetic material
- D. Non-magnetic material
Answer: B. Paramagnetic material — Above the Curie temperature, the thermal agitation overcomes the strong inter-atomic exchange interactions, causing the magnetic domains to disorient and the ferromagnetic material to lose its ferromagnetism, behaving like a paramagnetic material.
MCQ 6. The area enclosed by a hysteresis loop represents:
- A. The retentivity of the material.
- B. The coercivity of the material.
- C. The energy dissipated per unit volume during a magnetization cycle.
- D. The magnetic permeability of the material.
Answer: C. The energy dissipated per unit volume during a magnetization cycle. — The area of the hysteresis loop represents the energy lost per unit volume per cycle of magnetization and demagnetization in a magnetic material, primarily as heat.
MCQ 7. The angle of dip at the magnetic poles of the Earth is:
- A. 0°
- B. 45°
- C. 90°
- D. 180°
Answer: C. 90° — At the magnetic poles, the Earth's magnetic field lines are perpendicular to the surface, causing the dip needle to stand vertically, indicating an angle of dip of 90°.
MCQ 8. If a bar magnet is cut into two equal halves perpendicular to its length, the pole strength of each piece:
- A. Doubles
- B. Halves
- C. Remains the same
- D. Becomes zero
Answer: C. Remains the same — When a bar magnet is cut perpendicular to its length, new poles are induced at the cut ends, and each piece acts as a complete magnet. The pole strength of each new magnet remains the same as that of the original magnet.
MCQ 9. The relation between magnetic field B, magnetic intensity H, and magnetization M is given by:
- A. B = μ₀(H - M)
- B. B = μ₀H + M
- C. B = μ₀(H + M)
- D. B = μ₀(M - H)
Answer: C. B = μ₀(H + M) — The total magnetic field (B) inside a material is the sum of the magnetic field due to the external magnetizing field (μ₀H) and the magnetic field due to the magnetization (μ₀M) of the material itself.
MCQ 10. Which of the following is true for diamagnetic materials?
- A. They are strongly attracted by magnetic fields.
- B. Their magnetic susceptibility is large and positive.
- C. They are almost independent of temperature.
- D. They align themselves parallel to the external magnetic field.
Answer: C. They are almost independent of temperature. — Diamagnetic materials are characterized by a weak repulsion from magnetic fields, and their magnetic properties are largely independent of temperature because their induced magnetic moments are temporary and oppose the external field.
MCQ 11. Outside a bar magnet, magnetic field lines emerge from the ____ pole and enter the ____ pole.
- A. South, North
- B. North, South
- C. East, West
- D. West, East
Answer: B. North, South — Conventionally, magnetic field lines are depicted as originating from the North pole and terminating at the South pole outside a magnet, forming continuous closed loops.
MCQ 12. A magnetic dipole of moment M is placed in a uniform magnetic field B. The potential energy of the dipole is minimum when the angle between M and B is:
- A. 0°
- B. 90°
- C. 180°
- D. 45°
Answer: A. 0° — The potential energy of a magnetic dipole in a magnetic field is given by U = -M ⋅ B = -MB cosθ. Potential energy is minimum when cosθ is maximum (i.e., +1), which occurs at θ = 0°, meaning M is aligned parallel to B.
MCQ 13. The relation between relative permeability (μr) and magnetic susceptibility (χ) is:
- A. μr = 1 + χ
- B. μr = 1 - χ
- C. μr = χ - 1
- D. μr = χ
Answer: A. μr = 1 + χ — Relative permeability (μr) indicates how much a material concentrates magnetic flux. It is related to magnetic susceptibility (χ), which measures how much a material becomes magnetized in an applied field, by the equation μr = 1 + χ.
MCQ 14. According to Curie's Law, the magnetic susceptibility (χ) of a paramagnetic material is:
- A. Directly proportional to temperature.
- B. Inversely proportional to temperature.
- C. Independent of temperature.
- D. Directly proportional to the square of temperature.
Answer: B. Inversely proportional to temperature. — Curie's Law states that for paramagnetic materials, the magnetic susceptibility is inversely proportional to the absolute temperature, meaning χ ∝ 1/T.
MCQ 15. For making permanent magnets, materials should have:
- A. High retentivity and high coercivity.
- B. High retentivity and low coercivity.
- C. Low retentivity and high coercivity.
- D. Low retentivity and low coercivity.
Answer: A. High retentivity and high coercivity. — Permanent magnets require materials that retain a strong magnetization (high retentivity) even after the external field is removed and resist demagnetization (high coercivity).
MCQ 16. At the magnetic equator, the angle of dip is approximately:
- A. 0°
- B. 45°
- C. 60°
- D. 90°
Answer: A. 0° — At the magnetic equator, the Earth's magnetic field lines are parallel to the surface, causing the dip needle to lie horizontally, indicating an angle of dip of 0°.
MCQ 17. The magnetic field strength at a point on the axial line of a short bar magnet at a distance r from its center is proportional to:
- A. r
- B. 1/r
- C. 1/r²
- D. 1/r³
Answer: D. 1/r³ — For a short bar magnet, the magnetic field strength on its axial line varies as 1/r³, where r is the distance from the center of the magnet.
MCQ 18. If a magnetic needle is free to rotate in a horizontal plane, it will align itself in the direction of:
- A. Earth's total magnetic field.
- B. Earth's horizontal component of magnetic field.
- C. Earth's vertical component of magnetic field.
- D. Geographic North-South direction.
Answer: B. Earth's horizontal component of magnetic field. — A magnetic needle free to rotate in a horizontal plane aligns itself along the horizontal component of the Earth's magnetic field, defining the magnetic meridian.
MCQ 19. The SI unit of magnetic flux is:
- A. Tesla
- B. Weber
- C. Henry
- D. Ampere-meter
Answer: B. Weber — The SI unit for magnetic flux is the Weber (Wb), named after Wilhelm Eduard Weber.
MCQ 20. The angle between the geographic meridian and the magnetic meridian at a place is called:
- A. Angle of dip
- B. Angle of inclination
- C. Angle of declination
- D. Angle of latitude
Answer: C. Angle of declination — The angle of declination is the angle between the geographic meridian (true North) and the magnetic meridian (direction of a compass needle) at a particular location.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.