Course

Fundamentals of Physics, II

Yale University

This course serves as a continuation of Fundamentals of Physics I (PHYS 200), providing an in-depth exploration of essential physics topics suited for students with a solid foundation in both physics and mathematics.

Course topics include:

  • Electricity and magnetism
  • Electrostatics and electric fields
  • Capacitance and resistance
  • Circuits and their components
  • Geometrical and wave optics
  • Fundamentals of quantum mechanics

The course is structured into modules focusing on theoretical concepts, mathematical formulations, and practical applications to reinforce learning. Students will engage with various principles, from Coulomb's law to Maxwell's equations, culminating with an introduction to quantum mechanics.

Course Lectures
  • Electrostatics
    Ramamurti Shankar

    This module introduces the concept of electrostatics, beginning with the fundamental nature of electric charge and its interactions. Students will learn about:

    • Coulomb's Law and its applications
    • Principle of superposition for calculating forces
    • Charge conservation and quantization
    • Understanding charge distributions

    Through detailed discussions and examples, students will gain a comprehensive understanding of how electrostatic forces operate in various contexts.

  • Electric Fields
    Ramamurti Shankar

    This module delves into electric fields, introducing the concept as a fundamental aspect of electrostatic interactions. Key topics include:

    • The nature of electric fields and their significance
    • Field lines and their representation
    • Electric dipoles and the concept of dipole moment

    Students will explore how electric fields are generated by charged objects and how they affect other charges placed within the field.

  • In this module, students will further explore electric fields, focusing on Gauss's Law. Key elements include:

    • Understanding charge density and electric flux
    • Application of Gauss's Law to spherical charge distributions
    • Calculating electric fields from various charge configurations

    This understanding will be crucial for analyzing more complex electrical systems and phenomena in future modules.

  • Continuing with Gauss's Law, this module discusses its applications to conductors and insulators. Key topics include:

    • Derivation and limitations of Gauss's Law
    • Electric fields around conductors and insulators
    • Application of Gauss’s Law to various geometries

    This module is essential for understanding how electric fields behave in real-world materials.

  • This module introduces the concept of electric potential and its connection to energy conservation. Topics covered include:

    • Review of the law of conservation of energy
    • Deriving the work-energy theorem
    • Understanding electric potential in electrostatics

    Students will learn how the electric potential is related to electric fields and how energy is conserved in electric systems.

  • Capacitors
    Ramamurti Shankar

    In this module, students will explore the principles of capacitors, focusing on their role in storing charge and energy. Key areas include:

    • Definition and significance of capacitance
    • Calculating capacitance for different configurations
    • Understanding the behavior of capacitors in circuits

    This foundational knowledge is essential for understanding complex electrical circuits and energy storage systems.

  • This module discusses resistance in electrical circuits, detailing the forces acting on electric currents. Key topics include:

    • Understanding electric potential distribution in conductors
    • Image charges and their applications
    • Analyzing RC circuits and their energetics

    Students will learn how resistance impacts current flow and how to analyze circuits effectively.

  • Circuits and Magnetism I
    Ramamurti Shankar

    This module introduces more complex electric circuits and the fundamental principles of magnetism. Key topics include:

    • Basic concepts underlying magnetism
    • The relationship between electric charges and magnetic fields
    • The Lorentz force on a charge and its implications

    Students will explore how electric fields interact with magnetic fields and the fundamental equations governing magnetostatics.

  • Magnetism II
    Ramamurti Shankar

    This module continues the discussion on magnetism, focusing on the Law of Biot-Savart and its applications. Key points include:

    • The magnetic field produced by electric currents
    • Calculating magnetic fields for loops and infinite wires
    • Understanding Ampere's Law and its derivation

    Students will learn how to apply these laws to practical problems in magnetism and electrical engineering.

  • Ampere's Law
    Ramamurti Shankar

    This module further explores Ampere's Law, applying it to calculate magnetic fields in symmetric geometries. Key components include:

    • Finding magnetic fields generated by currents in solenoids
    • Understanding how magnetism converts mechanical energy to electrical work
    • Introducing Lenz's and Faraday's Laws

    Students will gain insights into the principles that govern the interaction of electricity and magnetism.

  • Lenz's and Faraday's Laws
    Ramamurti Shankar

    This module investigates Lenz's and Faraday's Laws further, focusing on their implications and applications. Key areas include:

    • The electric effect of changing magnetic fields
    • Operation and energy accounting of electric generators
    • Introduction to inductance and energy density in magnetic fields

    Students will understand how these laws demonstrate the interdependence of electric and magnetic phenomena.

  • LCR Circuits—DC Voltage
    Ramamurti Shankar

    This module focuses on LCR circuits with DC voltage, discussing the roles of inductors as energy storage devices. Key topics include:

    • Reviewing inductors and their functions
    • Analyzing inductive circuits and their behavior
    • Understanding LCR circuits driven by DC sources

    Students will learn how inductance affects circuit dynamics and energy transfer.

  • LCR Circuits—AC Voltage
    Ramamurti Shankar

    This module transitions to LCR circuits with AC voltage, incorporating complex numbers to analyze circuit behavior. Key components include:

    • The mathematics of LCR circuit theory for AC currents
    • Understanding impedance and its implications
    • Exploring resonance and variable capacitance using radios

    Students will gain a comprehensive understanding of the behavior of circuits under alternating current.

  • This module delves into Maxwell's Equations and their significance in understanding electromagnetic waves. Key points include:

    • Solving Maxwell's Equations and their physical meanings
    • Deriving the energy and intensity carried by electromagnetic waves
    • Understanding the consistency of Maxwell's equations with relativity

    Students will learn how these equations form the foundation of classical electromagnetism and wave theory.

  • Ray or Geometrical Optics I
    Ramamurti Shankar

    This module introduces the principles of ray optics, focusing on geometric optics as an approximation to wave theory. Topics include:

    • Understanding light as an electromagnetic phenomenon
    • Principles of reflection and refraction
    • Using Fermat's Principle of Least Time to derive optical results

    Students will learn how geometric optics provides practical insights into light behavior in various scenarios.

  • Ray or Geometrical Optics II
    Ramamurti Shankar

    This module continues the study of ray optics, using ray diagrams to analyze light behavior with mirrors and lenses. Key areas include:

    • Investigating parabolic and spherical mirrors
    • Understanding lens behavior and focal points
    • Examining the concept of magnifying lenses

    Students will learn how to apply ray diagrams to predict and analyze optical phenomena.

  • Wave Theory of Light
    Ramamurti Shankar

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

    • Young's double slit experiment and its implications
    • Understanding interference and diffraction of light
    • Analyzing grating and crystal diffraction patterns

    Students will explore how wave theory challenges classical notions of light and provides a deeper understanding of optical phenomena.

  • This module introduces quantum mechanics, beginning with key experiments that challenge classical physics. Topics include:

    • The double slit experiment and its implications for Newtonian mechanics
    • The de Broglie relation between wavelength and momentum
    • The photoelectric effect and Compton scattering

    Students will learn about the wave function, probability interpretation, and the uncertainty principle, marking the transition to quantum theory.

  • Quantum Mechanics II
    Ramamurti Shankar

    This module further examines quantum mechanics, focusing on the double slit experiment with electrons. Key topics include:

    • The implications of wave behavior for particles
    • The uncertainty principle and its significance
    • Probability density functions for electrons

    Students will deepen their understanding of quantum behavior and the duality of matter, building on previous concepts.

  • Quantum Mechanics III
    Ramamurti Shankar

    This module emphasizes the completeness of the wave function in describing a particle's properties. Key areas include:

    • Measurement and its effect on the wave function
    • Quantization of momentum for particles
    • Understanding the implications for quantum states

    Students will explore how measurement affects quantum systems and the significance of wave functions in quantum mechanics.

  • This module outlines measurement theory and states of definite energy in quantum mechanics. Key topics include:

    • Extracting odds for different momentum values from a wave function
    • Finding states of definite energy using the Schrödinger Equation
    • Analyzing the particle in a box model

    Students will learn how differential equations govern quantum systems, enhancing their understanding of energy quantization.

  • This module revisits the particle in a box concept and introduces quantum tunneling. Key areas of focus include:

    • Allowed energy states for particles in confined spaces
    • Analyzing scattering problems and quantum tunneling phenomena
    • Understanding the implications of kinetic energy and barriers

    Students will explore the fascinating world of quantum mechanics, including tunneling effects that defy classical expectations.

  • This module introduces the time-dependent Schrödinger Equation, a fundamental concept in quantum dynamics. Key topics include:

    • The analogy of the Schrödinger Equation to Newton's second law
    • Predicting future behavior from initial wave functions
    • The significance of stationary states in quantum systems

    Students will gain insights into predicting quantum behavior and understanding the dynamics of quantum systems.