Electromagnetism

Electromagnetism is a fundamental force, combining analysis of electric and magnetic phenomena. Our study in electrical engineering, electromagnetics, takes a fairly applied approach. Electromagnetism forms the theoretical and rigorous foundations for many constructs in electrical engineering, including photonics, circuit analysis, and electronics.

We can further divide the field into electrostatics, magnetostatics and electrodynamics. The idea is that:

• Stationary charges produce time-invariant electric fields, i.e., electrostatics.
• Steady currents (constant magnitude of $i$) produce time-invariant magnetic fields, i.e., magnetostatics.

An x represents something coming out of the page, while a . represents something going into the page.

Key concepts

• Maxwell’s equations
• Materials
  • Semiconductor
  • Conductor
  • Dielectric
    • Polarisation
    • Dielectric breakdown
  • Permittivity
  • Permeability
• Electromagnetic boundary conditions

Electrostatics

• Electric charge
  • Conservation of charge
• Coulomb’s law
• Electric field
  • Gauss’ law
    • Gaussian surface
  • Electric dipole
• Potential
  • Poisson’s equation
  • Laplace’s equation
  • Far-field approximation
• Current
  • Current density
• Ohm’s law
  • Resistance
  • Resistivity
  • Conductance
  • Conductivity
• Power
  • Joule’s law
• Capacitance
• Method of images
• Energy

Magnetostatics

• Magnetic force
• Magnetic field
  • Biot-Savart law
  • Hall effect
  • Magnetic dipole
  • Ampere’s law
• Magnetic vector potential
  • Poisson’s equation
  • Laplace’s equation
• Magnetism
• Magnetisation

Electrodynamics

• Faraday’s law
• Lenz’s law

Applications

• Printed circuit board
  • Electromagnetic interference
• Wireless communications
• Radio-frequency circuit
• Radar
• Medical imaging
• Quantum computing

Constants

The electrostatic constant $k$:

$$k=\frac{1}{4\pi {ϵ}_0}=8.99\times 10^9\frac{N\cdot m^2}{C^2}$$

The quantised elementary charge of an electron $e$:

$$e=1.602\times 10^{-19}C$$

The permittivity constant ${ϵ}_0$:

$${ϵ}_0=8.85\times 10^{-12}\frac{C^2}{N\cdot m^2}$$

The permeability of free space ${\mu }_0$:

$${\mu }_0=4\pi \times 10^{-7}H\cdot m^{-1}=1.25637\times 10^{-6}N\cdot A^{-2}$$

Resources

• Introduction to Electrodynamics, by David J. Griffiths
• Classical Electrodynamics, by John David Jackson
• Fundamentals of Applied Electromagnetics, by Umberto Ravaioli and Fawwaz Ulaby

Related courses

• ECE110 — Electrical Fundamentals
• ECE221 — Electric and Magnetic Fields