Entrance Examination in Physics

for students to be readmitted after expulsion or be transferred from other universities to MIPT

Test Format

The entrance test shall take the form of a combination of a written and oral examination.

1. The exam takes place in accordance with the Regulation on the readmission after expulsion and transfer from other organizations and the Regulation on the procedure for conducting entrance examinations at MIPT.

2. The total written test time is 3 hours.

3. The written test card includes problems on topics specified in the below List of Topics:

- for semester 2, topic 1 through topic 9;

- for semester 3, topic 1 through topic 19;

- for semester 4, topic 1 through topic 33;

- for semester 5, topic 1 through topic 42;

- for semesters 6 through 8, all topics specified in the List of Topics.

4. After the written test being completed, face-to-face discussion of the written part is held with each applicant. Examiners have the right to ask supplementary questions on the topics specified in the List of Topics depending on the semester applicants intend to readmit after expulsion or transfer to:

- for semester 2, topic 1 through topic 9;

- for semester 3, topic 1 through topic 19;

- for semester 4, topic 1 through topic 33;

- for semester 5, topic 1 through topic 42;

- for semesters 6 through 8, all topics specified in the List of Topics.

Entrance Examination in Physics

List of Topics

1. Newton's laws. Inertial and non-inertial reference frames.
2. Galilean relativity principle and Einstein relativity principle. Lorentz transformations. Invariance of the interval.
3. Laws of conservation of energy and momentum. Elastic and inelastic collisions.
4. Equation of motion of a material particle in relativistic mechanics. Momentum and energy of material particle.
5. Law of universal gravitation and Kepler's laws. Motion of bodies in gravitational field.
6. Law of conservation of angular momentum. Moment equation. Rotation of a rigid body about a fixed axis. Gyroscopes.
7. Ideal fluids. Continuity equation. Bernoulli’s equation.
8. Law of viscous fluid flow. Poiseuille formula. Reynolds number and its physical meaning.
9. Elastic deformations. Young's modulus and Poisson's ratio. Strain energy.
10. Ideal gas law, its explanation based on molecular-kinetic theory. Van der Waals equation.
11. Quasistatic process. First law of thermodynamics. Heat and Work. Internal energy. Enthalpy.
12. Second law of thermodynamics. Carnot cycle. Entropy and Law of degradation of energy. Ideal gas entropy.
13. Thermodynamic potentials. Equilibrium conditions of a thermodynamic system.
14. Maxwell and Boltzmann distributions.
15. Heat capacity. Equipartition of energy. Temperature dependence of heat capacity of gases.
16. Phase transitions. Clapeyron-Clausius equation. State-transition diagrams.
17. Transfer phenomena: diffusion, thermal conductivity, and viscosity. Transfer coefficients in gases. Steady-state heat conduction equation.
18. Surface tension. Laplace formula. Free energy and internal energy of the surface.
19. Fluctuations. Brownian motion. Einstein relation.
20. Coulomb Law. Gauss’s law in differential and integral forms. Circuital law in static electric field. Potential. Poisson’s equation.
21. Electrostatic field in substance. Polarization vector, electric induction. Boundary conditions for vectors E and D.
22. Magnetic field of direct current in vacuum. Basic equations of static magnetic field in vacuum. Biot-Savart law. Ampere force. Lorentz force.
23. Magnetic field in matter. Basic equations of static magnetic field in matter. Boundary conditions for vectors B and H.
24. Ohm's law for DC circuit. Transient phenomena in electrical circuits.
25. Electromagnetic induction in moving and stationary conductors. Induction electromotive force. Self-inductance and mutual inductance. Reciprocity theorem.
26. Maxwell’s equations in integral and differential forms. Displacement current. Constitutive relations.
27. Law of conservation of energy for electromagnetic field. Poynting vector. Electromagnetic field momentum.
28. Quasi-stationary currents. Free and forced oscillations in electrical circuits. Resonance in an AC circuit. Tuned circuit Q-factor and its energy meaning.
29. Spectral decomposition of electrical signals. Spectra of oscillations modulated in amplitude and phase.
30. Electrical fluctuations. Shot noise and thermal noise. Sensibility limit of electrical measuring instruments.
31. Electromagnetic waves. Wave equation. Helmholtz equation.
32. Electromagnetic waves in waveguides. Critical frequency. Cavity resonators.
33. Plasma. Plasma frequency. Plasma permittivity. Debye screening distance.
34. Wave interference. Time and spatial coherence. Uncertainty relation.
35. Huygens-Fresnel principle. Fresnel zones. Fresnel diffraction and Fraunhofer diffraction. Limit of applicability of geometrical optics.
36. Spectral instruments (prism, diffraction grating, Fabry-Perot interferometer) and their main characteristics.
37. Diffraction-limited resolution of optical and spectral instruments. Rayleigh criterion.
38. Spatial Fourier transform in optics. Diffraction on sine-wave grating. Abbey theory of image formation.
39. Principles of holography. Gabor hologram. Inclined reference beam hologram. Thick holograms.
40. Wave packet. Phase and group velocities. Rayleigh formula. Classical dispersion theory. Normal and abnormal dispersion.
41. Polarization of light. Brewster’s angle. Optical phenomena in uniaxial crystals.
42. X-ray diffraction. Bragg formula. Refractive index for X-rays.
43. Quantum nature of light. Outer photoemission. Einstein’s equation. Compton effect.
44. Spontaneous and stimulated radiation. Inverse population. Laser operating principle.
45. Black-body radiation. Planck formula, Wien law and Stefan-Boltzman law.
46. Wave-particle duality. De Broglie’s waves. Experiments of Davisson-Germer and Thomson on electron diffraction.
47. Wave function. Position operator and momentum operator. Average values of physical quantities. Uncertainty principle for position and momentum measurement. Schrödinger equation.
48. Hydrogen-like atom structure. Energy levels and their degeneracy. Emission spectrum of atomic hydrogen.
49. Stern-Gerlach experiments. Electron spin. Orbital and spin magnetic moments of electron.
50. Particle identity. Wave function symmetry with respect to permutation of particles. Bosons and fermions. Pauli exclusion principle. Electronic structure of atoms. Periodic Table.
51. Fine and hyperfine structures of optical spectra. Selection rules for the absorption and emission of photons by atoms.
52. Zeeman effect in weak magnetic fields.
53. Zeeman effect in strong magnetic fields.
54. Nuclear and electron magnetic resonances.
55. Law of radioactive decay. Half-life and lifetime.
56. Particle tunneling through a potential barrier. Alpha decay. Geiger-Nuttall law and its explanation.
57. Types of beta decay. Explanation of the continuity of energy spectrum of decay electrons. Neutrino.
58. Nuclear reactions. Compound nucleus. Cross section of non-resonant reactions. Bethe law.
59. Resonant nuclear reactions. Breit-Wigner formula.
60. Neutron-induced nuclear fission. Operation principle of nuclear reactor on thermal neutrons.
61. Uncertainty relation for energy and time. Estimation of lifetime of virtual particles, radii of strong and weak interactions.
62. Fundamental interactions and fundamental particles (leptons, quarks and carriers of interactions). Quark structure of hadrons.

Resources

1. Samuel J. Ling et al. University Physics, vol.1-3.

2. Arthur Beiser, Concepts of Modern Physics , 6th edition (2003).

3. Richard Feynman, Lectures on Physics, vol. 1-3.

4. Berkeley Physics Course, vol.1-5.

5. A. N. Matveev, Course of General Physics, vol.1-4 (1989).

6. E. R. Huggins, Physics-2000, Parts I, II.

7. I. E. Irodov, Problems in General Physics (1988).

Further Reading (in Russian)

1. Сивухин Д.В. Общий курс физики, Т. 1-5 М.: Физматлит (2003).

2. Сборник задач по общему курсу физики, Т. 1-3 /под ред. В.А. Овчинкина, М.: Физматкнига (2013).

3. Кингсеп А.С., Локшин Г.Р., Ольхов О.А. Основы физики. Курс общей физики . Т. 1-2, М.: Физматлит (2001)