Physics 2023 Paper II 50 marks Explain

Q7

(a) Explain classical theory of diamagnetism. Show that the susceptibility of diamagnetic substances is directly proportional to the atomic number. Why all the electrons in an atom contribute to diamagnetism ? 5+8+2=15 (b) Derive an expression for the specific heat of a solid based on the Debye theory and show how it agrees with the experimental values. What is the most important assumption of Debye theory in comparison to Einstein theory ? Is there any drawback of Debye theory ? 15+3+2=20 (c) With a neat circuit diagram, explain the working of Wien-Bridge oscillator. 15

हिंदी में प्रश्न पढ़ें

(a) प्रतिचुंबकत्व के चिरप्रतिष्ठित सिद्धांत की व्याख्या कीजिए । दर्शाइए कि प्रतिचुंबकीय पदार्थों की प्रवृत्ति सीधे परमाणु संख्या के समानुपाती होती है । एक परमाणु के सभी इलेक्ट्रॉन प्रतिचुंबकत्व में योगदान क्यों करते हैं ? 5+8+2=15 (b) डिबाई सिद्धांत से एक ठोस पदार्थ की विशिष्ट ऊष्मा के लिए व्यंजक प्राप्त करें और दिखाइए कि प्रायोगिक मानों से यह कितना संगत है । आइंस्टाइन सिद्धांत की तुलना में डिबाई सिद्धांत में सबसे महत्वपूर्ण अभिधारणा क्या है ? डिबाई सिद्धांत में क्या कोई कमी है ? 15+3+2=20 (c) एक स्पष्ट परिपथ आरेख के साथ वीन-ब्रिज दोलक की कार्य प्रणाली की व्याख्या कीजिए । 15

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Directive word: Explain

This question asks you to explain. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

See our UPSC directive words guide for a full breakdown of how to respond to each command word.

How this answer will be evaluated

Approach

The directive 'explain' demands clear exposition with logical flow across all three parts. Allocate approximately 30% time/words to part (a) on diamagnetism (15 marks), 40% to part (b) on Debye theory (20 marks), and 30% to part (c) on Wien-Bridge oscillator (15 marks). Structure: begin each part with defining the core concept, proceed through derivations with intermediate steps shown, and conclude with physical significance and limitations.

Key points expected

  • Part (a): Larmor precession explanation, derivation of χ = -μ₀NZe²⟨r²⟩/(6mₑ), proportionality to Z via electron count, and explanation of why all electrons contribute (closed shells, no net paramagnetism)
  • Part (b): Debye frequency distribution g(ω) ∝ ω², derivation of Cᵥ = 9R(T/θ_D)³∫₀^(θ_D/T) x⁴eˣ/(eˣ-1)²dx, T³ law at low T and Dulong-Petit at high T, comparison with Einstein's single frequency assumption
  • Part (c): Wien-Bridge circuit with four resistors and two capacitors, frequency formula f = 1/(2πRC), Barkhausen criterion (R₃/R₄ = 2), amplitude stabilization via lamp or diodes
  • Debye theory assumption: continuous spectrum of frequencies up to ω_D vs Einstein's single ω_E; Debye's acoustic phonon approximation
  • Drawbacks of Debye theory: fails at intermediate temperatures, neglects optical phonons, assumes isotropic solids and linear dispersion
  • Experimental verification: specific heat data for copper, lead, diamond showing T³ region and Debye temperature extraction

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Precise statements of Larmor theorem for (a), correct phonon density of states for (b), and accurate Barkhausen criterion for (c); correctly identifies that diamagnetism is universal while paramagnetism requires unpaired electronsGenerally correct concepts but with minor errors like confusing diamagnetic and paramagnetic response, or misstating the Debye cutoff conditionFundamental misconceptions such as attributing diamagnetism to unpaired electrons, or treating Einstein and Debye theories as identical
Derivation rigour25%12.5Complete derivations: induced magnetic moment from Faraday's law and Larmor frequency for (a); full Debye integral setup with proper limits and variable substitution for (b); loop gain analysis leading to frequency and amplitude conditions for (c)Derivations with gaps in steps, missing justification for key substitutions, or algebraic errors that don't affect final resultMissing derivations entirely, or derivations with critical errors like wrong dimensional analysis, incorrect integration limits, or invalid assumptions
Diagram / FBD15%7.5Neat, labeled Wien-Bridge circuit showing all four arms (R₁C₁ series, R₂C₂ parallel, R₃, R₄), ground reference, amplifier symbol, and output points; clear indication of positive and negative feedback pathsCircuit diagram present but with missing labels, incorrect component placement, or unclear feedback topologyNo diagram, or diagram with fundamental errors like wrong bridge configuration, missing amplifier, or confused RC network topology
Numerical accuracy15%7.5Correct numerical factors in all derived expressions: 1/6 in diamagnetic susceptibility, 9R and correct integral limits in Debye formula, factor of 2 in amplitude condition; proper handling of Debye temperature valuesMinor numerical errors in coefficients or constants that don't completely invalidate the derivationSerious numerical errors like wrong powers of temperature, incorrect factors of 2π, or magnitude errors in susceptibility expression
Physical interpretation25%12.5Clear explanation of why diamagnetism is weak and universal; physical meaning of Debye temperature as cutoff for acoustic phonons and its material dependence; why Wien-Bridge needs amplitude stabilization and frequency selectivity; connects to Indian solid-state research contextSome physical insight present but superficial treatment of limitations or missing connection between theory and measurable quantitiesPurely mathematical treatment with no physical explanation, or incorrect interpretation of what the derived quantities represent experimentally

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