Notes in Electromagnetism

• 01
  Maxwell's equations
  • Electric and magnetic potentials
  • Gauge transformations (non-uniqueness of potentials)
  • Maxwell's equations in terms of potentials
  • Maxwell's equations in Lorenz gauge
  • Delta function
  • Properties of delta function
  • Problems
    Maxwell's equations in terms of F_{\mu \nu}
    • Problems on delta function
  
  
• 02
  Statement of conservation of charge
  • Maxwell's equations for static case
  • Electrostatics
  • Green's function: potential due to a unit point charge
  • Evaluation of potential due to a point charge
  • Point charge: potential, electric field, force, energy
  • Problems
    charge densities of some simple geometries in terms of delta function and theta function
    • Electric dipole
  
  
• 03
  Electric potential and electric fields
  • Line charge
    • Potential due to a uniformly charged line segment
    • Electric field due to a uniformly charged line segment
    • Electric field due to a uniformly charged line segment: Again
  • Surface charge
    • Potential due to a uniformly charged disc
    • Electric field due to a uniformly charged disc
  • Volume charge
    • Potential due to a uniformly charged sphere
    • Electric field due to a uniformly charged sphere
  • Problems
    Infinite line charge as limit case of finite
    • General problems
  
  
• 04
  Differential vector calculus: gradient, divergence, curl
  • Integral vector calculus: line, suface, volume integral
  • Gradient theorem
  • Divergence theorem
  • Curl theorem
  • Integral vector calculus and electrostatics
  • Gauss's law: infinite line charge, infinite suface charge, uniform charge on sphere
  • Problems
    Problems on vector calculus
    • Problems on Gauss's law
  
  
• 05
  Work done to move a point charge
  • Potential energy
  • Potential energy due to a charge distribution
  • Conductors
  • Capacitors
  • Parallel plate capacitor
  • Problems
    Problems on work and potential energy
    • Problems on capacitance
  
  
• 06
  Boundary conditions on the surface of a conductors
  • Boundary value problems
  • Method of images: infinite conducting plane
  • Problems
    Conducting sphere: method of images
    • Capacitance due to two long cylindrical conductors
  
  
• 07 (in 3 files)
  Magnetostatics
  • Biot-Savart law
  • Magnetic potential and field due to a current carrying line segment Magnetic potential and field due to a finite solenoid Magnetic potential and field due to a circular wire
  • Problems
    Rotating charged spherical shell: a model for an elementary particle with magnetic dipole moment
    • Problems on vector potential
    • Problems on Biot-Savart law
  
  
• 08
  Ampere's law
  • Long wire, long sheet
  • Infinite solenoid
  • Toroid
  • Magnetic force
  • Hall effect
  • Problems
    Problems on Ampere's law
    • Problems on magnetic force
  
  
• 09
  Canonical momentum, electric energy and magnetic energy
  • Canonical momentum, electric energy and magnetic energy: Again
  • Magnetostatic energy
  • Magnetostatic energy of a current loop in an external field
  • Inductance
  • Problems
    Force, torque and work done on a current loop in a constant magnetic field
    • Mutual inductance of two parallel wires
  
  
• 10
  Electric and magnetic dipole moment
  • Force on an atom
  • Force on a macroscopic body
  • Macroscopic Maxwell's equations
  • Point electric dipole moment (time independent)
  • Point electric dipole moment (time dependent)
  • Point magnetic dipole moment
  • Problems
    Magnetic dipole moment due to a circular current carrying wire
    • Potential and electric field due to a time independent electric dipole moment
    • Stationary, time dependent electric dipole moment
    • Potential and magnetic field due to a magnetic dipole moment (time independent)
    • Other problems
  
  
• 11
  Electrically polarized object of finite size: volume charge density and surface charge density
  • Magnetically polarized object of finite size: volume current density and surface current density
  • Uniformly electrically polarized sphere: potential and electric field
  • Uniformly magnetically polarized sphere: magnetic potential and magnetic field
  • Problems (in 4 files)
    Linearly (radially) electrically polarized sphere: electric potential and electric field
    • Magnetically polarized infinite long cylinder: magnetic potential and magnetic field Solution to problem 5 Solution to problem 4 Solution to problem 4.11 in Griffiths
  
  
• 12
  Elementary model to understand Ohm's law
  • Faraday's law
  • Induced current
  • Induced current due to variation in $B$, $A$, and $\theta$
  • Problems
    Problems on Faraday's law
  
  
• 13
  Electric and magnetic Potential
  • Gauge
  • Radiation gauge, Lorentz gauge
  • Maxwell's equations in terms of potentials in Lorentz gauge
  • Solution to Green's function in Lorentz gauge
  • Potentials in terms of the Green function: Lienard Wickart potentials
  • Problems (in 2 files)
    Inhomogeneous wave equations satisfied by electric and magnetic fields
    • Electric and magnetic potential due to a point charge moving with a constant velocity Solution to problem 2
  
  
• 14 (page 8 missing)
  Potentials in the radiation approximation
  • Fields in the radiation approximation
  • Radiation field due to a point charge
  • Radiation field due to a nonrelativistic point charge
  • Problems
    Radiation due to an oscillating nonrelativistic point particle
    • Radiation due to a nonrelativistic point particle moving in a circle
    • Radiation due to a uniformly accelerating nonrelativistic point particle
  
  
• 15
  Statement of conservation of energy and momentum
  • Angular distribution of radiated power
  • Power radiated by a nonrelativistic charged particle: Larmor's formula
  • Power radiated by a nonrelativistic electric dipole
  • Problems (in 2 files)
    Problems on nonrelativistic radiation Solution
  
  
• 16
  Maxwell's equations
  • Electromagnetic waves in vacuum
  • Electromagnetic waves in matter (in absence of free charges)
  • Electromagnetic waves in conductors