Mini courses

Electromagnetic Theory Complete Mini Course

A structured mini course covering vector calculus, electrostatics, magnetostatics, Maxwell equations, and electromagnetic waves for ECE students.

Visual

Vector CalcElectrostaticsMagnetostaticsMaxwell Eq.WavesM1M2M3M4M5StartComplete

Course overview

This course covers electromagnetic theory from vector calculus foundations through to wave propagation in unbounded and bounded media. The progression is: coordinate systems and vector operators, electrostatics with Gauss's law and potential, magnetostatics with Ampere's law, time-varying fields and Maxwell's equations, and finally plane wave propagation and transmission lines. Students who complete the course can apply Gauss's law and Ampere's law to symmetric configurations, compute electric and magnetic potentials, derive and apply the wave equation, and analyze transmission line behavior using the telegrapher equations.

Details

Target audience: Third-year B.Tech ECE students taking Electromagnetic Theory or Fields and Waves, and GATE aspirants covering the Electromagnetics section.

Duration: 13 to 16 hours across 5 modules

Prerequisites

  • Vector algebra and dot and cross products
  • Calculus: partial derivatives and multiple integrals
  • Basic physics: Coulomb's law and magnetic force concepts

Learning outcomes

  • Express vector fields in Cartesian, cylindrical, and spherical coordinates and compute gradient, divergence, and curl
  • Apply Gauss's law to find electric fields for charge distributions with planar, cylindrical, or spherical symmetry
  • Use Ampere's law to compute magnetic fields for infinite wires, solenoids, and toroids
  • State Maxwell's four equations in both integral and differential form and explain the physical meaning of each
  • Derive the wave equation from Maxwell's equations and compute phase velocity, attenuation, and skin depth for a given medium
  • Analyze transmission lines using the telegrapher equations and calculate reflection coefficient and VSWR

Modules

Module 1: Vector Calculus and Coordinates
Topics
  • Cartesian, cylindrical, and spherical coordinate systems
  • Gradient, divergence, and curl operators
  • Divergence theorem and Stokes' theorem
  • Line integrals and surface integrals
  • Helmholtz theorem and vector field decomposition
Article slugs
coordinate-systems-cylindrical-sphericalgradient-divergence-curldivergence-stokes-theorem
Lab slug: vector-calculus-visualization-lab
Module 2: Electrostatics
Topics
  • Coulomb's law and electric field due to charge distributions
  • Gauss's law in integral and differential form
  • Electric potential and relationship to field
  • Laplace and Poisson equations
  • Boundary conditions at dielectric interfaces
Article slugs
coulombs-law-electric-fieldgauss-law-applicationslaplace-poisson-equation
Lab slug: electrostatics-field-lab
Module 3: Magnetostatics
Topics
  • Biot-Savart law and magnetic field calculations
  • Ampere's law and applications to symmetric configurations
  • Magnetic vector potential
  • Magnetic boundary conditions at material interfaces
  • Inductance calculation for coils and toroids
Article slugs
biot-savart-lawamperes-law-applicationsinductance-calculation
Lab slug: magnetostatics-field-lab
Module 4: Maxwell's Equations
Topics
  • Faraday's law and displacement current
  • Maxwell's equations in differential and integral form
  • Poynting theorem and energy flow
  • Wave equation derivation from Maxwell's equations
  • Time-harmonic fields and phasor representation
Article slugs
faradays-law-displacement-currentmaxwells-equations-summarypoynting-theorem-energy
Lab slug: maxwells-equations-lab
Module 5: Waves and Transmission Lines
Topics
  • Uniform plane wave propagation in lossless and lossy media
  • Reflection and transmission at normal incidence
  • Skin depth and surface impedance
  • Transmission line equations and characteristic impedance
  • Standing wave ratio and impedance matching
Article slugs
plane-wave-propagationreflection-transmission-coefficientstransmission-line-analysis
Lab slug: transmission-line-lab