Lecture

Magnetism II

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.


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.