Fields and Forces
Start with Coulomb's law, electric fields, Gauss's law, and simple circuits (Ohm's law, Kirchhoff's rules).
Electromagnetism
Maxwell's equations, electric and magnetic fields, electromagnetic waves, and circuits — the physics that underlies all modern technology.
Overview
Electromagnetism is the branch of physics describing electric and magnetic fields, their interactions with matter, and the electromagnetic waves that include light, radio, and X-rays. James Clerk Maxwell unified electricity, magnetism, and optics into four compact equations in the 1860s — one of the greatest achievements in the history of science.
The field divides into electrostatics (stationary charges), magnetostatics (steady currents), electrodynamics (time-varying fields), and the study of electromagnetic waves and their interactions with matter.
Core Concepts
Electric Fields and Coulomb's Law
Coulomb's law describes the force between two stationary point charges: F = kq₁q₂/r². The electric field E = F/q quantifies the force per unit charge at any point in space, visualised as field lines pointing away from positive charges and toward negative charges. Gauss's law relates the total electric flux through a closed surface to the enclosed charge.
Magnetic Fields and the Lorentz Force
Moving charges generate magnetic fields, described by the Biot-Savart law and Ampère's law. The Lorentz force law F = q(E + v × B) gives the total electromagnetic force on a charge moving in combined electric and magnetic fields. Magnetic monopoles do not exist — field lines always form closed loops.
Maxwell's Equations
Maxwell's four equations are the complete classical description of electromagnetism:
- Gauss's law: ∇·E = ρ/ε₀ — electric fields diverge from charges
- Gauss's law for magnetism: ∇·B = 0 — no magnetic monopoles
- Faraday's law: ∇×E = −∂B/∂t — changing B induces E
- Ampère-Maxwell law: ∇×B = μ₀J + μ₀ε₀∂E/∂t — currents and changing E produce B
Taking the curl of the last two yields the electromagnetic wave equation, predicting waves that travel at c = 1/√(μ₀ε₀) ≈ 3×10⁸ m/s — the speed of light.
Electromagnetic Induction
Faraday's law: a changing magnetic flux induces an EMF. Lenz's law specifies its direction — opposing the change that caused it. This is the principle behind generators, transformers, and inductive charging. Self-inductance describes how a coil opposes changes in its own current.
Learning Pathways
Induction and Circuits
Cover Faraday's and Lenz's laws, inductance, capacitance, AC circuits, and the LC oscillator.
Maxwell's Theory
Master Maxwell's equations in differential form, electromagnetic waves, and the connection to special relativity.
Key Articles
Maxwell's Equations
A complete derivation and physical interpretation of all four Maxwell equations.
Read →The Photoelectric Effect
Einstein's explanation that launched quantum theory — light as photons.
Read →The Aharonov-Bohm Effect
How electromagnetic potentials affect quantum phases even where fields are zero.
Read →The Faraday Effect
Magnetic fields rotate the polarisation of light — a deep link between EM and optics.
Read →The Kerr Effect
How electric fields alter the refractive index of a medium.
Read →The Plasma Frequency
How free electrons in a plasma respond to electromagnetic waves.
Read →Related Calculators
Frequently Asked Questions
What do Maxwell's equations describe?
How electric and magnetic fields are generated by charges and currents, how they interact, and how changing fields produce one another — predicting light as an electromagnetic wave.
What is the difference between electric potential and electric field?
E is a force-per-unit-charge vector; V is a scalar potential energy per unit charge. They relate via E = −∇V.
Why does a changing magnetic field create an electric field?
Faraday's law of induction: changing magnetic flux induces an EMF. This drives generators, transformers, and wireless charging.
What is an electromagnetic wave?
A coupled oscillation of E and B fields propagating at c ≈ 3×10⁸ m/s. All light — radio, visible, X-rays — is electromagnetic radiation.