# Investigate Maxwell’s contribution to the classical theory of electromagnetism

Light is electromagnetic radiation.

It is the portion of the electromagnetic spectrum which is visible to the  naked eye.

Maxwell’s contribution to classical theory of electromagnetism:

• Maxwell was inspired by Faraday’s and Ampere’s work.
• He consolidated his work on Electricity and Magnetism, and in 1865 published A Dynamical Theory of Electromagnetic Field. [https://royalsocietypublishing.org/doi/10.1098/rstl.1865.0008]
• In this paper, he published 20 equations which were called “General Equations of the Electromagnetic Field”.
• With these equations Maxwell showed that electricity and magnetism were different manifestations of the same phenomena – Electromagnetism.
• Heaviside and Hertz independently reduced the 20 equations to 4 fundamental equations, which described Electricity and Magnetism in terms of electric and magnetic fields.
• These four equations are popularly called Maxwell’s equations today.

Maxwell’s Equations:

• [also known as Gauss’s Law]
• This shows that the electric flux passing through a closed surface depends on the total charge present within the closed surface. Coulomb’s inverse square law about electric field can be derived from Gauss’s law.
• This shows that magnetic flux passing through a closed surface is always zero.
• [also known as Faraday’s Law]
• This describes the electric field induced due to a changing magnetic field. This electric field is in a loop.
• [also known as Ampere-Maxwell Law]
• This describes the magnetic field that is created either due to a moving charge or changing electric field.
• Faraday’s Law and Ampere-Maxwell law show how electric and magnetic fields are interlinked and dependent on each other.

These four laws form the basis for the classical theory of electromagnetism.

Maxwell showed that on the basis of his equations of electromagnetic field, a propagating  oscillating electric and magnetic field is expected.

• He thus predicted the existence of Electromagnetic waves.
• He also predicted that the light is also electromagnetic wave

Using the equations of electromagnetic field, Maxwell calculated the speed of electromagnetic wave.

• Maxwell derived the wave equations for electromagnetic waves using equations of electromagnetic field
• The speed of the wave according to the derived wave equation was :
• where , = permeability of free space
• = permittivity of free space
• The calculated value of the speed of electromagnetic wave according to this prediction was in accordance with the speed of light that was experimentally calculated before.

Extract from Physics Stage 6 Syllabus © 2017 NSW Education Standards Authority (NESA)