# Fundamentals of Physics, II

Yale University

This is a continuation of Fundamentals of Physics, I (PHYS 200), the introductory course on the principles and methods of physics for students who have good preparation in physics and mathematics. This course covers electricity, magnetism, optics and quantum mechanics.

• ##### Electrostatics
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The course begins with a discussion of electricity. The concept of charge is introduced, and the properties of electrical forces are compared with those of other familiar forces, such as gravitation. Coulomb's Law, along with the principle of superposition, allows for the calculation of electrostatic forces from a given charge distribution. 00:00 - Chapter 1. Review of Forces and Introduction to Electrostatic Force 15:20 - Chapter 2. Coulomb's Law 21:09 - Chapter 3. Conservation and Quantization of Charge 26:15 - Chapter 4. Microscopic Understanding of Electrostatics 33:21 - Chapter 5. Charge Distributions and the Principle of Superposition Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Electric Fields
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The electric field is introduced as the mediator of electrostatic interactions: objects generate the field which permeates all of space, and charged objects in the field experience a force with magnitude proportional to their charge. Several instructive examples are given, including the field of an electric dipole and the notion of the electric dipole and dipole moment. The notion of field lines is introduced. 00:00 - Chapter 1. Review of Charges 16:34 - Chapter 2. Electric Fields 33:55 - Chapter 3. Electric Field Lines 40:18 - Chapter 4. Electric Dipoles Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Gauss's Law I

Fundamentals of Physics, II (PHYS 201) The electric field is discussed in greater detail and field due an infinite line charge is computed. The concepts of charge density and electric flux are introduced and Gauss's Law, which relates the two, is derived. It is applied to the study of the electric field generated by a spherical charge distribution. 00:00 - Chapter 1. Review of Electric field concepts 15:02 - Chapter 2. Electric field due to an infinite line of charge 28:41 - Chapter 3. The Infinite Sheet and Charge Density 44:29 - Chapter 4. Gauss' Law Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Gauss's Law and Application to Conductors and Insulators
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Lecture begins with a recap of Gauss's Law, its derivation, its limitation and its applications in deriving the electric field of several symmetric geometries—like the infinitely long wire. The electrical properties of conductors and insulators are discussed. Multiple integrals are briefly reviewed. 00:00 - Chapter 1. Derivation of Gauss' Law 21:12 - Chapter 2. The Electric Field due to a Spherical Distribution of Charge 44:47 - Chapter 3. Electric Field due to an Infinitely Long Wire 51:39 - Chapter 4. Electric Conductors and Insulators Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### The Electric Potential and Conservation of Energy
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The law of conservation of energy is reviewed using examples drawn from Newtonian mechanics. The work-energy theorem is derived from first principles and used to initiate a discussion of the vector calculus underlying the law of conservation of energy. 00:00 - Chapter 1. Review of Electrostatics 03:49 - Chapter 2. Review of Law of Conservation of Energy 08:13 - Chapter 3. Deriving the Work-Energy Theorem and the Law of Conservation of Energy 59:33 - Chapter 4. Electric Potential Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Capacitors
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The electric potential is defined for the electric field. It is introduced as an integral of the electric field making the field the derivative of the potential. After discussing the ideas of electric potential and field as presented in the previous lecture, the concept of capacitance is introduced as a means of storing charge and energy. 00:00 - Chapter 1. Review of Electric Potential 15:52 - Chapter 2. Advantages of Electric Potential, V 43:31 - Chapter 3. Conductors as Equipotentials 61:46 - Chapter 4. Capacitors Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Resistance

Fundamentals of Physics, II (PHYS 201) Lecture begins with a discussion of electric potential distribution in conductors. Image charges are introduced and exploited. Capacitance is explained in greater detail and illustrated using the parallel plate capacitor. The energy stored in the electric field is derived. The forces acting on an electric current flowing through a conducting wire are examined. The RC circuits and its energetics are discussed. The EMF due to a battery is explained. 00:00 - Chapter 1. Review of Image Charges 28:45 - Chapter 2. The Parellel Plate Capacitor 42:46 - Chapter 3. The Concept of Resistance Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Circuits and Magnetism I
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) After a description of more complicated electric circuits, the basic ideas underlying magnetism are discussed and the relationship between electrical charges and magnetic fields is explored. Magnetism is caused and experienced only by moving charges. The Lorentz force on a charge is described and used to deduce the force on a current carrying wire. The cyclotron and velocity selector are described. 00:00 - Chapter 1. Review of Electric Circuits 34:32 - Chapter 2. Introduction to Magnetism 45:29 - Chapter 3. Fundamental Equations of Magnetostatics 62:42 - Chapter 4. Force on a Current Carrying Wire Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Magnetism II
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The mechanism by which electric currents produce a magnetic field (Law of Biot-Savart) is discussed in greater detail. The field due to a single loop and an infinite wire are computed. Ampere's Law is derived. The operation of the DC electric motor is used to illustrate the torque generated on moving charges in a magnetic field. 00:00 - Chapter 1. Review of Magnetic Fields 14:00 - Chapter 2. Torque on Charge moving in Magnetic Field 20:56 - Chapter 3. Magnetic effects produced by electric currents 51:26 - Chapter 4. Ampere's Law Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Ampere's Law
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Ampere's Law is used to find the magnetic field generated by currents in highly symmetric geometries like the infinitely long wire and the solenoid. It is shown how magnetism can be used to convert macroscopic mechanical energy to do microscopic electrical work. Lenz's and Faraday's Laws are introduced. The latter says that a changing magnetic field generates a non-conservative electric field. 00:00 - Chapter 1. Review of Ampere's Law 08:46 - Chapter 2. Magnetic field generated by current in a solenoid 49:51 - Chapter 3. Lenz's Law 67:07 - Chapter 4. Faraday's Law Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Lenz's and Faraday's Laws
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The electric effect of a changing magnetic field is described using Faraday's Law. The direction of the current so generated is given by Lenz's Law. The operation and energy accounting of the generator are described. The concept of inductance is introduced. The Betatron is described as an example of Faraday's Law. Self and mutual inductance are introduced. The energy density in a magnetic field is derived. 00:00 - Chapter 1. Review of Lenz and Faraday's Law 25:37 - Chapter 2. The power generator 37:45 - Chapter 3. Mutual and self inductance 64:10 - Chapter 4. Energy density of a magnetic field Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### LCR Circuits—DC Voltage
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Like capacitors, inductors act as energy storage devices in circuits. The relationship between voltage, inductance and current in a variety of circuits with DC voltages is described. 00:00 - Chapter 1. Review of Inductors 04:46 - Chapter 2. Inductive Circuits 54:18 - Chapter 3. LCR Circuits driven by an Alternating Source Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### LCR Circuits—AC Voltage
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The mathematics underlying LCR circuit theory for AC currents is discussed. Complex numbers are used to convert differential equations to algebraic equations. The notion of impedance is introduced. The radio is used to illustrate the concepts of resonance and variable capacitance. The body of classical electromagnetism treated so far is reviewed and summarized. The displacement current is introduced, leading to the complete Maxwell equations. 00:00 - Chapter 1. Review of LCR Circuits 08:48 - Chapter 2. Impedance 17:39 - Chapter 3. Resonance and Variable Capacitance 68:03 - Chapter 4. Displacement current Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Maxwell's Equations and Electromagnetic Waves II
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The physical meaning of the components of the wave equation and their applications are discussed. The power carried by the wave is derived. The fact that, unlike Newton's laws, Maxwell's equations are already consistent with relativity is discussed. The existence of magnetism is deduced from a thought experiment using relativity. 00:00 - Chapter 1. Recap—Solving Maxwell's Equations 18:18 - Chapter 2. Deriving the Energy and Intensity of an Electromagnetic Wave 30:40 - Chapter 3. The Origin of Electromagnetic Waves 37:03 - Chapter 4. Relativity and Maxwell's Equations 51:44 - Chapter 5. Deducing the Presence of Magnetism Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Ray or Geometrical Optics I
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Geometric optics is discussed as an approximation to wave theory when the wavelength is very small compared to other lengths in the problem (such as the size of openings). Many results of geometric optics involving reflection, refraction (mirrors and lenses) are derived in a unified way using Fermat's Principle of Least Time. 00:00 - Chapter 1. Light as an Electromagnetic Phenomenon 07:17 - Chapter 2. Review of Geometrical (Classical) Optics 21:50 - Chapter 3. Fermat's Principle of Least Time and its Corollaries Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Ray or Geometrical Optics II
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Ray diagrams are used to investigate the behavior of light incident on mirrors and lenses. The principle of least time is used to show that all rays from an object in front of a concave mirror focus on the image point if they are not too far from the axis. The experiments describing the breakdown of geometric optics are discussed. 00:00 - Chapter 1. Parabolic and Spherical Mirrors 34:16 - Chapter 2. Lenses 43:34 - Chapter 3. Focal Point 63:56 - Chapter 4. Magnifying Lenses Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Wave Theory of Light
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Young's double slit experiment shows clearly that light is a wave. (In order to observe the wave behavior of light, the slit size and separation should be comparable or smaller than the wavelength of light.) Interference is described using real and complex numbers (in anticipation of quantum mechanics). Grating and crystal diffraction are analyzed. 00:00 - Chapter 1. Revisions to Geometric Optics 08:20 - Chapter 2. Young's double slit experiment 50:52 - Chapter 3. Interference and Diffraction of Light Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum Mechanics I: The Key Experiments and Wave-Particle Duality
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The double slit experiment, which implies the end of Newtonian Mechanics is described. The de Broglie relation between wavelength and momentum is deduced from experiment for photons and electrons. The photoelectric effect and Compton scattering, which provided experimental support for Einstein's photon theory of light are reviewed. The wave function is introduced along with the probability interpretation. The uncertainty principle is shown arise from the fact that the particle's location is determined by a wave and that waves diffract when passing a narrow opening. 00:00 - Chapter 1. Recap of Young's double slit experiment 09:10 - Chapter 2. The Particulate Nature of Light 23:15 - Chapter 3. The Photoelectric Effect 31:19 - Chapter 4. Compton's scattering 36:10 - Chapter 5. Particle-wave duality of matter 48:33 - Chapter 6. The Uncertainty Principle Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum Mechanics II
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) Lecture begins with a detailed review of the double slit experiment with electrons. The fate of an electron traversing the double slit is determined by a wave putting an end to Newtonian mechanics. The momentum and position of an electron cannot both be totally known simultaneously. The wave function is used to describe a probability density function for an electron. Heuristic arguments are given for the wave function describing a particle of definite momentum. 00:00 - Chapter 1. Review of Double Slit Experiment using Electrons 20:28 - Chapter 2. Heisenberg's Uncertainty Principle 42:32 - Chapter 3. The Probability Density Function of an Electron Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum Mechanics III
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The fact that the wave function provides the complete description of a particle's location and momentum is emphasized. Measurement collapses the wave function into a spike located at the measured value. The quantization of momentum for a particle on a ring is deduced. 00:00 - Chapter 1. Review of the Particle Wave Function 11:21 - Chapter 2. Particle on a Ring 56:25 - Chapter 3. The Measurement Postulate Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum mechanics IV: Measurement Theory, States of Definite Energy
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) It is shown how to extract the odds for getting different values of momentum from a generic wave function by writing it as a sum over functions of definite momentum. A recipe is given for finding states of definite energy, which requires solving a differential equation that depends on what potential the particle is experiencing. The particle in a box is considered and the allowed energies derived. 00:00 - Chapter 1. Review of Wave Functions 40:13 - Chapter 2. The Schrodinger Equation 54:20 - Chapter 3. Quantization of Energy 63:43 - Chapter 4. Particle in a Box Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum Mechanics V: Particle in a Box
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The allowed energy states of a free particle on a ring and a particle in a box are revisited. A scattering problem is studied to expose more quantum wonders: a particle can tunnel into the classically forbidden regions where kinetic energy is negative and a particle incident on a barrier with enough kinetic energy to go over it has a nonzero probability to bounce back. 00:00 - Chapter 1. Review of Wave Functions 08:48 - Chapter 2. Particle on a ring 19:11 - Chapter 3. Particle in a Box 54:00 - Chapter 4. Scattering Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.

• ##### Quantum Mechanics VI: Time-dependent Schrödinger Equation
Ramamurti Shankar

Fundamentals of Physics, II (PHYS 201) The time-dependent Schrödinger Equation is introduced as a powerful analog of Newton's second law of motion that describes quantum dynamics. It is shown how given an initial wave function, one can predict the future behavior using Schrödinger's Equation. The special role of stationary states (states of definite energy) is discussed. 00:00 - Chapter 1. The "Theory of Nearly Everything" 12:34 - Chapter 2. The time-dependent Schrodinger Equation 40:15 - Chapter 3. Stationary States Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Spring 2010.