Physics: Problems and Solutions
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The University of Virginia Physics PHd Qualifying Exam[]

All UVa physics PHd candidates must pass the UVa physics qualifier (qual) in order to continue on to receive a PHd. The qualifier covers four basic areas of physics;

  1. Classical Mechanics
  2. Thermodynamics & Statistical Mechanics
  3. Electricity & Magnetism
  4. Quantum Mechanics.

The last two sections are the major sections and are given twice as much weight as the first two.

Schedule[]

Traditionally, the qual has been offered at the beginning of the fourth semester (January) after having completed the required course work and again near the end of the fourth semester(April) for those students that did not pass the first time. For 2007 and later the qualifier has been restructured. It is intended that the qualifier will now be administered after the second semester (May) and again before the start of the third semester (August) as a last chance. As part of the transition, the exam will be offered three times during 2007; January, May, and August. The test is split over two days with one day covering Classical and E&M, the other covering Stat. Mech. and Quantum. Each testing day consists of six questions (two from the minor section and four from the major section) and four hours are given to solve the questions.

Problems and Solutions[]

Classical Mechanics[]

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  7. Cubic pendulum
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  9. Space station orbit
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Statistical Mechanics[]

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  8. Entropy, work, and Helmholtz free energy
  9. Grand Canonical Partition function
  10. Ferromagnet
  11. Bose-Einstein Condensation temperature
  12. Landau quantization
  13. Stirling cycle
  14. Spin 1/2 particles in magnetic field
  15. Ideal gas of massless Bosons
  16. Phase equilibrium and Clausius-Clapeyron equation
  17. Adiabatic expansion, Carnot Cycle
  18. Ensemble of spins in B-field
  19. P-V curve
  20. Compression of ideal gas
  21. Heat Capacity of ideal gas
  22. Blackbody radiation
  23. Gas leaking through a small hole
  24. Neutron star
  25. Free energies for mass on elastic thread
  1. Centrifuge
  2. Ionized gas
  3. Entropy of mixing
  4. Joule-Thompson effect
  5. Isothermal compression
  6. Equipartition of energy
  7. Max work from cooling
  8. Two connected systems
  9. Relation between Cp and Cv
  10. Blackbody radiation
  11. Two gases mixing
  12. Joule-Kelvin (Thompson) coefficient
  13. Adiabatic expansion, isothermal compression
  14. Gibbs free energy and entropy of monatomic gas
  15. Enthalpy from equation of state and heat capacity
  16. Expansion of saturated vapor
  17. System of 2-state particles
  18. Internal energy, constant number of particles
  19. Partition function and distribution function
  20. Adiabatic and isothermal nonsense
  21. Crazy heat engine
  22. Two gases in separate containers

Electricity and Magnetism[]

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  9. Meissner effect in super conducting sphere
  10. Atomic spectral line
  11. Cylindrical capacitor in liquid dielectric
  12. Circular polarized light incident o bound electron
  13. Rectangular waveguide
  14. Two rotating charged spheres
  15. Potential inside a box
  16. Index of refraction of the ionosphere
  17. Cerenkov radiation
  18. Charge subjected to a wave described by vector potential
  19. Rectangular current loop
  20. Cylinder carrying current I
  21. Radiating particle in two inertial frames
  22. B-field and E-field in lab frame from moving frame
  23. Energy flux conservation in resistor
  24. Potential of dielectric sphere
  25. Skin depth
  26. Spherical cavity in a conductor
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Quantum Mechanics[]

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  10. Stark effect for hydrogen atom
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  19. Two electrons confined to a circle
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