Electricity and Magnetism

Two Forces, One Theory

Electricity and magnetism appear at first to be two separate phenomena. A charge at rest produces an electric force. A moving charge produces a magnetic force. James Clerk Maxwell unified these into a single electromagnetic theory in the 1860s — one of the greatest intellectual achievements in the history of physics.

Electric Charge and Coulomb's Law

Electric charge is a fundamental property of matter. Like charges repel; unlike charges attract. Coulomb's law gives the force between two point charges: it is an inverse-square law, just like gravity, but enormously stronger.

Electric Fields and Potential

The electric field is a vector that tells you the force per unit charge at each point in space. Gauss's law — one of Maxwell's four equations — relates the total electric flux through a closed surface to the enclosed charge.

Electric potential (voltage) is the potential energy per unit charge. Moving charges from low potential to high potential requires work. Electric field lines point from high to low potential.

Circuits

Electric current is the flow of charge. Ohm's law relates current to voltage through resistance. Kirchhoff's laws let you analyze complex circuits by applying conservation of energy and conservation of charge.

Capacitors store charge and energy in electric fields. Inductors store energy in magnetic fields. Resistor-capacitor and resistor-inductor circuits exhibit time-dependent behavior.

Magnetic Fields

Moving charges and current-carrying wires produce magnetic fields. The Biot-Savart law gives the field produced by a current element. Ampere's law — another of Maxwell's equations — relates the circulation of the magnetic field around a loop to the current passing through it.

Electromagnetic Induction

A changing magnetic field induces an electric field. This is Faraday's law. It is the principle behind generators, transformers, and inductive charging. Lenz's law tells you the direction of the induced current: it opposes the change that caused it.

Maxwell's Equations

Maxwell collected the four fundamental laws of electromagnetism, added a crucial correction term (the displacement current), and showed that they predict the existence of electromagnetic waves traveling at the speed of light. Light, radio waves, microwaves, X-rays, and gamma rays are all electromagnetic radiation.