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Physics 3 - Maxwell
Note from the Author
Table of Contents
What is this book
Historical facts
New aspects
Fully erroneous
Incorrectly interpreted

Physics 3 - Chapter 1
Equations
Complex vectors form
The Most General form
The General Solution

Physics 3 - Chapter 2
Solutions
Initial conditions
Non-homogeneous equation
Solution for three-directions
The four laws

Physics 3 - Supplement
Fermat's proof
Beal's conjecture
Pythagorean triples
Inertial mass
Gravity constans big G
What does the Moon look at?

Physics 3 - Final notes
Final notes

Physics 4 - New book
Entry

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Chapter 1.   Equations

1.1.  Symbols and notations used

     To denote vector variables, we will use:
arrow above a letter A⃗  , B⃗  , C⃗   or bold letters A, B, C .
Dot product (scalar) will be written as: A⃗  ∙ B⃗  and vector cross product as: A⃗  ╳ B⃗  .
     We will use nabla (del) operator ∇ as a vector for divergence operation ∇∙
and for curl operation  ∇╳ .

The values used in Maxwell’s equations are denoted as follows:
     
D     -      electric induction (C/m2)
ρ E    -       density of electric charge (C/m3)
B     -       magnetic induction (Wb/m2)
ρ M   -       density of magnetic charge (Wb/m3)
E     -       electric field strength (V/m)
JM   -       magnetic current density (V/m2)
H     -       magnetic field strength (A/m)
JE    -       electric current density (A/m2)
ϵ0    -       vacuum permittivity (F/m)
μ0    -       magnetic permeability of vacuum = 4π ·10-7 (H/m)
c     -      speed of light in vacuum wr1 [m/s]
letter “i” used in equations denotes imaginary variable wr2.



1.2.  The most general form of Maxwell’s equations

      We will deal with Maxwell’s equations in the form proposed by Heaviside and Gibbs and complemented with magnetic monopole and magnetic current. This is mathematically the most general form of theses equations.
      The problem of magnetic monopole real existence is not relevant mathematically concerning solutions of the equations.
      Maxwell’s equations in most general form are presented by following formulas:
wr01, (1.1)
wr02, (1.2)
wr03, (1.3)
wr04, (1.4)
wr5a, (1.5a)
wr5b, (1.5b)

      The textbooks and publications which include introduction to Maxwell’s equations should use the above, since they present the essence of described phenomena in short and concise from. In addition, main equations (1.1-1.4) do not contain any coefficients, thus make them quite easy to memorize.
      If there is no need to use values of D⃗  and H⃗  we can use relation (1.5) in equation (1.4), therefore obtaining:
wr5c, which can be further divided by ϵ0  in addition using (1.5) in (1.1), we can derive Maxwell’s equations in a form shown below.
      However, this form is not easy to memorize:
wr06, (1.6)
wr07, (1.7)
wr08, (1.8)
wr09, (1.9)


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