# Maxwell

James Clerk Maxwell (1831 – 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation. He was the first to describe electricity, magnetism, and light as different manifestations of the same phenomenon, thereby laying the foundation for modern electromagnetic theory.

The Spectrum of Electromagnetic Energy

Maxwell demonstrated that light is just part of the energy spectrum extending from near direct current (DC) to the highest frequencies of electromagnetic energy traveling through free space. This spectrum includes a range of electromagnetic (EM) energy frequencies, all governed by the parameters μ₀ (permeability of free space) and ε₀ (permittivity of free space). These parameters determine how energy propagates through space and interact with it.

Fundamental Discoveries and Equations

Maxwell’s work revealed that EM energy consists of oscillating electric and magnetic fields. His equations describe how these fields are generated and interact by combining various laws into a cohesive group:

First: Gauss’s law for static electric fields – Electric fiends emanate from electric charges with an electrical charge there is an electrical field emanating from it. The strength of this field is proportional to e0. Static charges only affect other charges, not magnets:

∇⋅E=ρ/ε0

Where ∇·E is the divergence of the electric field, ε0 is the vacuum permittivity and ρ is the total volume charge density (charge per unit volume).

Second: Gauss’s law for static magnetic fields – There are no magnetic (monopoles) charges in the universe. There is always as much field pointed in as there is pointed out. Static magnets will affect only other magnets, not charges:

∇⋅B=0

Where ∇·B is the divergence of the magnetic field.

Third: Faraday’s law states a changing (in time) magnetic field produces an electric field. A moving magnet will create an electrical field. A moving magnet it will affect a charge, creating a current of electricity.

∇xE = dB/dt

Where E is the electromotive force (emf) and dB is the magnetic flux.

Fourth: Ampere-Maxwell’s law states a changing electric field produces a magnetic field. The first term describes a moving charge it will generate a magnetic field. Two wires will be attracted to each other if they have a current flowing through them. The second term says a magnetic field is created by moving charges which are created by moving electrical fields (i.e., an electromagnetic wave is propagated). This term recognized the current flow through capacitors (displacement capacitance) can create magnetic fields, The idea that changing magnetic fields are created by changing electrical fields was Maxwell’s addition to Amperes law. This fourth equation is a wave equation.

∇×B = μ0J+ϵ0 ∂E/∂t

Where: E is the electric field, B is the magnetic field, ρ is the charge density, J is the current density, ϵ0​ is the permittivity of free space, and μ0​ is the permeability of free space.

Equations involving the speed and density of energy

Speed of energy:

c2 = 1/μ0ε0

Impedance of space:

Z0 = √(μ0/ε0)