A Dynamical Theory of the Electromagnetic Field

A Dynamical Theory of the Electromagnetic Field was the third of James Clerk Maxwell's papers concerned with electromagnetism. The theory was the first paper in which Maxwell's equations appeared. The concept of displacement current was introduced, so that it became possible to derive equations of electromagnetic wave. According to the comprehension of the major trend for the fundamental equations of electromagnetic fields, electromagnetic potential is not explicitly involved. In his original paper, the equations are compiled to two sets.

Maxwell's equations

Maxwell's 1865 formulation was in terms of 20 equations in 20 variables, and, in 1873, he attempted a quaternion formulation. The later change to the vector notation produced a symmetric mathematical representation that reinforced the perception of physical symmetries between the various fields. The equations express, respectively, how electric charges produce electric fields (Gauss's law), the experimental absence of magnetic charges, how currents produce magnetic fields (Ampere's law), and how changing magnetic fields produce electric fields (Faraday's law of induction).

The first set is

Electric density

• $\mathbf {E} =-\nabla \phi -{\frac {\partial \mathbf {A} }{\partial t}}$

Magnetic density

• $\mathbf {B} =\nabla \times \mathbf {A}$

The second set is

Electric charge

• $\nabla \cdot \mathbf {D} =\rho$

Current density

• $\nabla \times \mathbf {H} -{\frac {\partial \mathbf {D} }{\partial t}}=\mathbf {J}$

where:

ρ is the free electric charge density, not including dipole charges bound in a material,

B is the magnetic flux density (in units of tesla, T), also called the magnetic induction,

D is the electric displacement field ,

E is the electric field,

H is the magnetic field strength,

J is the current density,

Quotes

Maxwell (1865) wrote:

This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according to electromagnetic laws.

Futher reading

• Maxwell, James Clerk, "A Dynamical Theory of the Electromagnetic Field". 1865.
• James C. Maxwell , Thomas F. Torrance, "A Dynamical Theory of the Electromagnetic Field". March, 1996. ISBN 1579100155

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