Free self-study course · Prof. Gökhan Çınar
Electromagnetic
Fields and Waves
Course notes, fully solved problems and interactive simulations for electromagnetic fields and waves: from vector calculus and Coulomb's law through magnetostatics and Maxwell's equations to plane waves, waveguides and cavity resonators. A small set of basic laws, and everything else derived from them.
Contents
The site follows the book chapter by chapter. Every section develops the theory first and ends with problems, home exercises, further exercises and worked examples, each with a step-by-step solution you can reveal one step at a time.
Introduction
What electromagnetics is about, the electromagnetic model, source and field quantities, units and constants, notation.
Mathematical Background
Vectors and vector algebra, the nabla operator, the Cartesian, cylindrical and spherical coordinate systems, and the integral theorems.
Electrostatics
Coulomb's law, Gauss's law, the electrostatic potential, and fields in material media: boundary conditions, images, energy and capacitance.
Magnetostatics
Lorentz force, Biot–Savart's law and the vector potential, magnetic media, inductance and energy, Ohm's law, and magnetic circuits.
Maxwell's Equations
From statics to electrodynamics: the displacement current, Faraday's law of induction, the continuity equation, the wave equation and time-harmonic waves.
Plane Electromagnetic Waves
Uniform plane waves in free space and in different media, power flow and the Poynting vector, and reflection and transmission at plane boundaries.
- 6.1 Plane Waves in Free Space (coming soon)
- 6.2 Propagation in Different Media (coming soon)
- 6.3 Normal Incidence (coming soon)
- 6.4 Oblique Incidence (coming soon)
Waveguides and Cavities
Guided waves: TEM, TM and TE modes in parallel-plate, rectangular, circular, coaxial and dielectric guides, microstrip lines and cavity resonators.
- 7.1 Fields in Waveguides (coming soon)
- 7.2 Parallel-Plate Waveguides (coming soon)
- 7.3 Rectangular Waveguides (coming soon)
- 7.4 Circular Waveguides (coming soon)
- 7.5 Coaxial Waveguides (coming soon)
- 7.6 Dielectric Waveguides (coming soon)
- 7.7 Microstrip Lines (coming soon)
- 7.8 Cavity Resonators (coming soon)
Learn by experimenting
The simulations run entirely in your browser: drag charges, push a dielectric into a capacitor, paint electrodes and watch Laplace's equation being solved. Every tool shows the formula it computes, so you can check your hand calculation against it.
Vector Algebra
Drag two vectors and see their sum, difference, dot product (as a projection) and cross product (as an oriented area).
SimulationGradient and Directional Derivative
Contour map of a scalar hill with its gradient field. Move a point and a direction to see the directional derivative.
SimulationVector Field Explorer
Arrows, divergence and curl maps of 2-D vector fields, with a probe that shows net outflow and paddle-wheel rotation, and a loop that checks the divergence and Stokes theorems numerically.
SimulationCoordinate Systems in 3-D
Rotate a 3-D scene, move a point in Cartesian, cylindrical or spherical coordinates and watch the local unit vectors and coordinate surfaces.
SimulationPoint-Charge Playground
Drag point charges, change their values and see the Coulomb forces, field vectors, field lines and equipotentials update instantly.
SimulationBuilding a Continuous Charge from Point Charges
Approximate a line, ring or disk charge by N point charges and watch the field at a point converge to the integral.