Maxwell's are:

dpt[muon*H>]=-curl[E>];
dpt[epsilon*D>]=curl[H>]-J>;
div[epsilon*E>]=VD
& div[muon*H>]=0.

Further Inspection is being done upon the "exact-validity" of the equations that has been invented [collected and modified] by MAXWELL ....

A program has been set by by my personell - as a consultant in Communications and Electronics and Owner of Nobel Prize [PQED] - to investigate the exact formula-set, especially after the announce of the explore of the 7th Quark and the connection done between Electromagnetics and Gravitics.

Isn't there a factorial div[J>] in the equation of the curl [stroke] of the magnetic field flux density?

A good question to begin with.

Amr Morsi .. CRWA [\David ].

[latex]\nabla \cdot \mathbf{E}=\frac{\rho}{\varepsilon_{0}}[/latex]

[latex]\nabla \cdot \mathbf{B}= 0[/latex]

[latex]\nabla \times \mathbf{E}= -\frac{\partial\mathbf{B}}{\partial t}[/latex]

[latex]\nabla \times \mathbf{B}= \mu_{0}\mathbf{J}+\mu_{0}\varepsilon_{0}\frac{\partial\mathbf{E}}{\partial t}[/latex]

Just for the practice and to avoid confusion to new members. These are the most common differential representations.


Where

[latex]\nabla \cdot [/latex] --> divergence operator
[latex]\nabla \times [/latex] --> curl operator
[latex]\mathbf{E}[/latex] --> Electric field
[latex]\mathbf{B}[/latex] --> Magnetic field
[latex]\rho[/latex] --> charge desity
[latex]\varepsilon_{0}[/latex] --> electric constnat permittivity of free space
[latex]\mu_{0}[/latex] --> magnetic constant permiability of free space
[latex]\mathbf{J}[/latex] --> total current density
[latex]\frac{\partial}{\partial t}[/latex] --> is the partial derrivative wrto time



For macroscopic diff you replace the first with

[latex]\nabla \cdot \mathbf{D}= \rho_{f}[/latex]

and the last with
[latex] \nabla \times \mathbf{H} = \mathbf{J}_{f} + \frac{\partial\mathbf{D}}{\partial t}[/latex]

[latex]\rho_{f}[/latex] and [latex]\mathbf{J}_{f}[/latex] ie with the subscript f are the free (rather than the total) charge density and current density.

[latex] \mathbf{H}[/latex] ---> magnetic field intensity
[latex] \mathbf{D}[/latex] ---> electric flux density

Edited February 6, 201312 yr by imatfaal
correction - thanks elfmotet

Imatfaal, the second term in the last of the four equations should be positive. If it's not positive then you can't get the wave equation out of Maxwell's equations.

Edited February 6, 201312 yr by elfmotat

Imatfaal, the second term in the last of the four equations should be positive. If it's not positive then you can't get the wave equation out of Maxwell's equations.

Corrected in original post many thanks. that's the problem with cutting and pasting from one line to the next, copied the partial derivative to avoid retyping and took the operator with it.