Why Are There 8 Maxwell Equations for 6 Field Variables?

[abrowaqas]

I have almost completed whole the derivation of maxwell equations but didn't get the answer that what was the purpose of Maxwell Equations. where these are beneficial. where we can apply them. at what point maxwell Eqs. fails? All four maxwell equations are actually Faraday's and Gauss's laws equations then what is the difference between them. kindly give an explanation of maxwell equation and their purpose in physics.

 

[dulrich]

Well, that's an open ended question!

Maxwell's laws describe the dynamics of the electromagnetic field, i.e., how the field changes with time in response to the motion of charges. All electrical, magnetic and optical phenomena are fundamentally described by these four equations (in principle). Every macroscopic force except gravity is, at its root, electromagnetic in nature.

Quantum Electrodynamics offers a correction to Maxwell's equations on the small scale, but they are correct in both special and general relativity.

The reason they are called Maxwell's is because he was the one to put the last puzzle piece in place (see http://en.wikipedia.org/wiki/Displacement_current). With this he was able to prove that light was electromagnetic.

 

[AJ Bentley]

Maxwell's equations are a distillation of centuries of pains-taking work by the scientists who preceded him.
He encapsulated and summarised their work in four, simple elegant and easily remembered formulae.
If you know and understand them, you don't need to remember all the odd little laws and rules such as Amperes, Gauss, Lenz's Boit-Savart etc. etc.

 

[abrowaqas]

good explanation dulrich..

 

[GRDixon]

at what point maxwell Eqs. fails?

For an interesting take on this question, check out Sect. 28-1 in "The Feynman Lectures on Physics," V2. Feynman states, "...this tremendous edifice, which is such a beautiful success in explaining so many phenomena, ultimately falls on its face."

 

[jtbell]

If you know and understand them, you don't need to remember all the odd little laws and rules such as Amperes, Gauss, Lenz's Boit-Savart etc. etc.

You better remember the first two, because they are two of Maxwell's equations!

 

[phywjc]

You better remember the first two, because they are two of Maxwell's equations!

they have no essential difference

 

[Dr Lots-o'watts]

where these are beneficial. where we can apply them.

Since they have been formulated (1880-something), they can be used as the starting point for any problem that relates to electromagnetism (except for some quantum-scale cases).

 

[Bob S]

Since [Maxwell's equations] have been formulated (1880-something), they can be used as the starting point for any problem that relates to electromagnetism (except for some quantum-scale cases).

... and except for the Lorentz-force equation (F = I x B), which is the basis for electric motors.

Bob S

 

[cmos]

Before Maxwell, electricity, magnetism, and optics were all separate fields. Maxwell was the one who elucidated the unified theory electromagnetism. He was able to bring together scattered and previously unlinked theories under one body of knowledge. In doing so, he was able to state the fundamental laws that are today known as Maxwell's equations. The individual equations may carry other peoples' names, but it is the combined set of equations that is Maxwell's.

An interesting side note: The original Maxwell equations were actually 20 equations. Today, we don't consider some of them as truly fundamental and others are auxiliary. Also, vector analysis was yet to be invented during Maxwell's time. What we call Maxwell equations today, is largely due to the further studies by Hertz and Heaviside.

 

[a-tom-ic]

@Cmos:
Do you know a source of the original Maxwell equations? I'd love to look them up. (Hopefully i can read them)

 

[jtbell]

Try here:

On the Notation of Field Equations of Electrodynamics, by André Waser (PDF file)

 

[RedX]

While we're at it, could anyone answer this:

Maxwell's equation involves two vector equations and two scalar equations, for a total of 8 equations.

What if you took the gradient of the scalar equations, and added them to the vector equations?

You would then have 6 equations, still enough for the 6 components of the E and B fields.

In general, why are there 8 equations for 6 field variables?