Course

Fundamentals of Physics, II

Yale University

Fundamentals of Physics, II (PHYS 201) is designed for students with a solid background in physics and mathematics. This course serves as a continuation of Fundamentals of Physics, I (PHYS 200) and covers a range of topics:

  • Electricity and electrostatics
  • Magnetism and electromagnetic fields
  • Optics and wave theory
  • Quantum mechanics and wave-particle duality

Students will engage with concepts such as Coulomb's Law, electric fields, Gauss's Law, circuits, and the principles of quantum mechanics through detailed lectures and practical examples. The course materials are designed to provide a thorough understanding of the principles and methods of physics as they apply to real-world phenomena.

Course Lectures
  • Electrostatics
    Ramamurti Shankar

    This module introduces the fundamental concepts of electrostatics, focusing on the nature of electric charge and the forces between charged objects. Key topics include:

    • Coulomb's Law and its applications
    • Principle of superposition for charge distributions
    • Microscopic understanding of electrostatics

    The module aims to provide a solid foundation for understanding electric forces and their implications in various physical scenarios.

  • Electric Fields
    Ramamurti Shankar

    This module delves into electric fields, which act as the medium for electrostatic interactions. Students will explore:

    • The concept and definition of electric fields
    • Field lines and their significance
    • Electric dipoles and their properties

    Through various examples, the module illustrates how charged objects generate electric fields and how these fields influence other charges within them.

  • This module presents Gauss's Law, a fundamental principle linking electric fields and charge distributions. Key discussions include:

    • Derivation of Gauss's Law
    • Applications to spherical charge distributions
    • Electric fields due to infinite line charges and sheets

    Students will apply Gauss's Law to solve electrostatic problems, solidifying their understanding of electric flux and charge density.

  • This module expands on Gauss's Law, focusing on its limitations and its applications in different geometries. Topics include:

    • Deriving Gauss's Law for various shapes
    • Electric fields of conductors and insulators
    • Review of multiple integrals in electrostatics

    By understanding how Gauss's Law applies to conductors and insulators, students will gain insights into the behavior of electric fields in different materials.

  • This module focuses on the electric potential and the law of conservation of energy. Key topics include:

    • Definition of electric potential and its relation to electric fields
    • Work-energy theorem and its derivation
    • Application of conservation of energy in electrostatic systems

    The module emphasizes the mathematical underpinnings of energy conservation and its implications in electric fields.

  • Capacitors
    Ramamurti Shankar

    This module introduces capacitors as devices for storing electric charge and energy. It covers:

    • Definition and function of capacitance
    • Relationship between electric potential and capacitance
    • Equipotential surfaces and their significance

    Students will learn how capacitors operate in circuits and their role in storing energy for later use.

  • This module examines resistance in conductors and the fundamental principles of current flow. Topics include:

    • Electric potential distribution in conductors
    • Concept of resistance and its role in circuits
    • RC circuits and battery EMF explanation

    Students will analyze how electric currents behave in different materials and the factors affecting resistance.

  • Circuits and Magnetism I
    Ramamurti Shankar

    This module introduces the concepts of circuits and basic principles of magnetism. Key areas of focus include:

    • Overview of complex electric circuits
    • Relationship between electric charges and magnetic fields
    • Introduction to Lorentz force on moving charges

    Students will explore how electricity and magnetism interact, leading to practical applications in circuit design.

  • Magnetism II
    Ramamurti Shankar

    This module continues the discussion on magnetism, focusing on how electric currents generate magnetic fields. Topics include:

    • Law of Biot-Savart and its applications
    • Magnetic fields due to loops and infinite wires
    • Introduction to Ampere's Law

    Students will understand the principles governing magnetism and its applications in various physical systems.

  • Ampere's Law
    Ramamurti Shankar

    This module focuses on Ampere's Law and its application to symmetric geometries for magnetic fields. Key discussions include:

    • Finding magnetic fields generated by wires and solenoids
    • Converting mechanical energy to electrical work
    • Introduction to Lenz's Law and Faraday's Law

    Students will learn how changing magnetic fields can induce electric fields, deepening their understanding of electromagnetism.

  • Lenz's and Faraday's Laws
    Ramamurti Shankar

    This module discusses Lenz's and Faraday's Laws, focusing on the electric effects of changing magnetic fields. Key topics include:

    • How to determine the direction of induced currents
    • Operation of generators and energy accounting
    • Concepts of self and mutual inductance

    Students will explore how these principles apply to real-world systems, such as generators and transformers.

  • LCR Circuits—DC Voltage
    Ramamurti Shankar

    This module covers LCR circuits with DC voltages, emphasizing inductors as energy storage devices. Key points include:

    • Relationships between voltage, inductance, and current
    • Analysis of LCR circuits driven by direct current
    • Practical applications in circuit design

    Students will learn how LCR circuits operate and how inductors contribute to energy storage and transfer.

  • LCR Circuits—AC Voltage
    Ramamurti Shankar

    This module focuses on LCR circuits with AC voltages, introducing the mathematics behind their theory. Key topics include:

    • Use of complex numbers to solve circuit equations
    • Definition and application of impedance
    • Concepts of resonance and variable capacitance

    Students will explore the implications of AC currents on circuit behavior and how these principles are applied in real-world systems.

  • This module discusses Maxwell's Equations and their relation to electromagnetic waves. Key discussions include:

    • Application of wave equations and their components
    • Power carried by electromagnetic waves
    • Consistency of Maxwell's equations with relativity

    Students will gain insights into how these equations govern the behavior of electromagnetic phenomena and their implications in modern physics.

  • Ray or Geometrical Optics I
    Ramamurti Shankar

    This module introduces geometrical optics, treating light as rays and exploring its behavior. Key topics include:

    • Reflection and refraction principles
    • Use of Fermat's Principle of Least Time
    • Applications of geometric optics in lenses and mirrors

    Students will learn how to analyze light behavior using ray diagrams and the underlying principles of optical systems.

  • Ray or Geometrical Optics II
    Ramamurti Shankar

    This module continues the study of geometrical optics, examining light interactions with mirrors and lenses. Key discussions include:

    • Ray diagrams for concave and convex mirrors
    • Understanding focal points and image formation
    • Applications of magnifying lenses

    Students will analyze the breakdown of geometric optics and its limitations, enhancing their understanding of optical principles.

  • Wave Theory of Light
    Ramamurti Shankar

    This module introduces the wave theory of light, emphasizing its wave-like behavior through experiments. Key topics include:

    • Young's double slit experiment and its implications
    • Interference patterns and their significance
    • Diffraction and the behavior of light in various contexts

    Students will explore how wave theory reconciles with classical optics, providing a comprehensive view of light behavior.

  • This module delves into quantum mechanics, discussing key experiments that challenge classical physics. Topics include:

    • Review of the double slit experiment with photons and electrons
    • Exploration of the photoelectric effect and Compton scattering
    • Introduction of the wave function and its probability interpretation

    Students will grasp the core concepts of wave-particle duality and the uncertainty principle, which redefine our understanding of matter.

  • Quantum Mechanics II
    Ramamurti Shankar

    This module continues the exploration of quantum mechanics, emphasizing the double slit experiment with electrons. Key discussions include:

    • Wave function as a probability density function
    • Understanding the implications of the uncertainty principle
    • Relationship between measurement and wave function collapse

    Students will deepen their understanding of quantum behavior and the principles governing particle interactions.

  • Quantum Mechanics III
    Ramamurti Shankar

    This module explores the complete description of a particle's location and momentum through the wave function. Key topics include:

    • Measurement and its effect on wave function collapse
    • Quantization of momentum for particles
    • Understanding the implications of wave functions in quantum mechanics

    Students will learn how wave functions model quantum behavior and the significance of measurement in quantum states.

  • This module introduces measurement theory in quantum mechanics, focusing on states of definite energy. Key discussions include:

    • Extracting momentum values from wave functions
    • Solving the Schrödinger Equation for states of definite energy
    • Understanding the particle in a box problem and its implications

    Students will explore the mathematical framework of quantum mechanics and how it applies to physical systems.

  • This module revisits critical concepts in quantum mechanics, particularly the particle in a box and scattering problems. Key topics include:

    • Understanding allowed energy states for free particles
    • Analyzing quantum tunneling and scattering phenomena
    • Exploring the implications of energy barriers in quantum mechanics

    Students will engage with quantum wonders that challenge classical intuitions and explore the probabilistic nature of quantum mechanics.

  • This module introduces the time-dependent Schrödinger Equation, a cornerstone of quantum dynamics. Key discussions include:

    • The analogy of the Schrödinger Equation to Newton's laws
    • Predicting future behavior from initial wave functions
    • Understanding stationary states and their significance

    Students will learn how quantum mechanics describes dynamic systems over time, enhancing their comprehension of quantum behavior.