## Maxwell’s Equations Summary: Electromagnetic Waves Predicted and Observed

Contents

- Electromagnetic waves consist of oscillating electric and magnetic fields and propagate at the speed of light \(c\). They were predicted by Maxwell, who also showed that
\(c=\cfrac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}},\)

where \({\mu }_{0}\) is the permeability of free space and \({\epsilon }_{0}\) is the permittivity of free space.

- Maxwell’s prediction of electromagnetic waves resulted from his formulation of a complete and symmetric theory of electricity and magnetism, known as Maxwell’s equations.
- These four equations are paraphrased in this text, rather than presented numerically, and encompass the major laws of electricity and magnetism. First is Gauss’s law for electricity, second is Gauss’s law for magnetism, third is Faraday’s law of induction, including Lenz’s law, and fourth is Ampere’s law in a symmetric formulation that adds another source of magnetism—changing electric fields.

## Glossary

### electromagnetic waves

radiation in the form of waves of electric and magnetic energy

### Maxwell’s equations

a set of four equations that comprise a complete, overarching theory of electromagnetism

*RLC* circuit

an electric circuit that includes a resistor, capacitor and inductor

### hertz

an SI unit denoting the frequency of an electromagnetic wave, in cycles per second

### speed of light

in a vacuum, such as space, the speed of light is a constant 3 x 10^{8} m/s

### electromotive force (emf)

energy produced per unit charge, drawn from a source that produces an electrical current

### electric field lines

a pattern of imaginary lines that extend between an electric source and charged objects in the surrounding area, with arrows pointed away from positively charged objects and toward negatively charged objects. The more lines in the pattern, the stronger the electric field in that region

### magnetic field lines

a pattern of continuous, imaginary lines that emerge from and enter into opposite magnetic poles. The density of the lines indicates the magnitude of the magnetic field