Electronics Engineering · CHAPTER 00 · FOCUSED LESSON

James Clerk Maxwell

One unified theory for electricity, magnetism, light and electromagnetic waves.

1860s · BritainALI'S NOTES · PAGES 8–9

Maxwell unified electricity, magnetism and light.

James Clerk Maxwell did more than collect earlier laws. He introduced the missing symmetry that allowed changing electric and magnetic fields to sustain an electromagnetic wave.

James Clerk Maxwell (1831–1879)Selected from Ali Chourba's original course document.

THE UNIFICATION

Separate observations become one field theory.

Maxwell assembled results associated with Coulomb, Gauss, Ørsted, Ampère and Faraday into a coherent mathematical framework. Electric and magnetic forces were no longer unrelated subjects; they became different manifestations of one electromagnetic interaction.

His crucial addition was the displacement-current term: a changing electric field can create a magnetic field even where no conduction current crosses the surface. This completed the symmetry with Faraday's result that a changing magnetic field creates an electric field.

THE FOUR IDEAS

What each equation says physically.

Gauss's law for electricity says electric charge is a source or sink of electric field. Gauss's law for magnetism says magnetic field lines form continuous loops—no isolated magnetic monopoles have been observed. Faraday's law says changing magnetic flux creates a circulating electric field. The Ampère–Maxwell law says current and changing electric flux create a circulating magnetic field.

Electric charge → electric-field divergence.
No magnetic monopoles → zero magnetic-field divergence.
Changing magnetic flux → induced electric field.
Current or changing electric flux → magnetic field.

THE PREDICTION

An oscillation can travel through space.

An oscillating charge creates changing electric and magnetic fields. Each changing field can regenerate the other, allowing a wave to propagate away from its source. Maxwell calculated its speed from the electric permittivity and magnetic permeability of free space.

The calculated value matched the known speed of light. Maxwell therefore concluded that light is an electromagnetic wave. Hertz later generated and detected longer-wavelength waves in the laboratory, turning the theoretical prediction into visible evidence.

FORMULAE & SI UNITS

Every symbol, defined.

Read the equation together with the physical meaning and SI unit of each parameter.

1 · Gauss's law for electricity

Electric charge is the source or sink of the electric field.

Symbol	Physical meaning	SI unit
∇ ·	Divergence operator: spatial spreading of a field	per metre (m⁻¹) as a differential operator
E	Electric field	volt per metre (V/m)
ρ	Volume electric-charge density	coulomb per cubic metre (C/m³)
ε₀	Vacuum electric permittivity	farad per metre (F/m)

2 · Gauss's law for magnetism

Magnetic field lines form closed loops; no isolated magnetic monopole has been observed.

Symbol	Physical meaning	SI unit
∇ ·	Divergence operator	per metre (m⁻¹) as a differential operator
B	Magnetic flux density	tesla (T)
0	No net magnetic source or sink	dimensionless zero

3 · Faraday's law in differential form

A changing magnetic field creates a circulating electric field; the minus sign expresses Lenz's law.

Symbol	Physical meaning	SI unit
∇ ×	Curl operator: local circulation of a field	per metre (m⁻¹) as a differential operator
E	Electric field	volt per metre (V/m)
B	Magnetic flux density	tesla (T)
t	Time	second (s)

4 · Ampère–Maxwell law

Magnetic fields are created by conduction-current density J and by a changing electric field.

Symbol	Physical meaning	SI unit
∇ ×	Curl operator	per metre (m⁻¹) as a differential operator
B	Magnetic flux density	tesla (T)
μ₀	Vacuum magnetic permeability	henry per metre (H/m)
J	Electric current density	ampere per square metre (A/m²)
ε₀	Vacuum electric permittivity	farad per metre (F/m)
E	Electric field	volt per metre (V/m)
t	Time	second (s)

Electromagnetic-wave speed in vacuum

The value predicted from the electric and magnetic constants matches the measured speed of light.

Symbol	Physical meaning	SI unit
c	Speed of light and electromagnetic waves in vacuum	metre per second (m/s)
μ₀	Vacuum magnetic permeability	henry per metre (H/m)
ε₀	Vacuum electric permittivity	farad per metre (F/m)

ORIGINAL SOURCE VISUALS

The document's own evidence and diagrams.

Maxwell equations from the course document — The four field relationships presented in Ali's notes.

Electromagnetic wave speed calculation — The electric and magnetic constants predict the propagation speed.

THE IDEA TO REMEMBER
Maxwell's deepest result was not a decorative wave; it was a testable prediction that light and radio are the same kind of electromagnetic phenomenon.

SOURCES

Charge, current and changing fields

PREDICTION

Self-propagating EM waves

IDENTIFICATION

Light is an EM wave

COURSE SOURCE · “ELECTRONICS AND TECHNOLOGY” · ALI CHOURBA