How Does Maxwell's Theory Relate to Newton's Classical Mechanics?

[Misr]

Maxwell's theory??

hi,people
1-I read that Maxwell's theory depends on classical mechanics of Newton so how??and which law it depends upon?

2-"Maxwell's theory can be applied on relatively big bodies" how?

 

[Dr Lots-o'watts]

1. Not sure about "dependent", but they are certainly consistent and complimentary. If a body has mass, you describe its mouvement with Newton's laws. If it has a charge, you describe the fields with Maxwell's equations. If it has both, you use both.

2. What do you mean by big? Unless you reach atomic or galactic scales, size is irrelevant to Maxwell's equations. They are for anything that has an electric field.

 

[Misr]

1. Not sure about "dependent", but they are certainly consistent and complimentary. If a body has mass, you describe its mouvement with Newton's laws. If it has a charge, you describe the fields with Maxwell's equations. If it has both, you use both.

great..just give me an example how they are complimentary
Maxwell said that a charged body in a circular path is in a state of continuous radiation
so what is the relation between this and Newton's laws??

 

[cragar]

If it is moving in a circular path it is accelerating , and accelerating charges emit light .
All tho this doesn't happen around an atom and Bohr tried to fix this by saying that an electron had discrete orbits .

 

[Born2bwire]

great..just give me an example how they are complimentary
Maxwell said that a charged body in a circular path is in a state of continuous radiation
so what is the relation between this and Newton's laws??

Not much actually. Technically, as the particle radiates, it draws off the energy from its kinetic energy. This could be modeled as a reaction-radiation pressure (you could think of this as the change in momentum that results when we emit a photon due to conservation of momentum). We could thus look at the radiation pattern and find the net effective force due to constant emission and then add that into our mechanics. However, we do not do this because the rate of emmission is so low that the impact on the trajectory of the particle is negligible. I recall that Jackson looks at the case of a linearly accelerating charge and notes how astronomical the amount of energies that need to be involved before we actually see a noticeable change in the trajectory due to the radiation.

 

[cragar]

So when the electron emits the photon does the gravitational pull of the electron go down, and is the gravitational field transferred to the photon .

 

[Petr Mugver]

hi,people
1-I read that Maxwell's theory depends on classical mechanics of Newton so how??and which law it depends upon?

2-"Maxwell's theory can be applied on relatively big bodies" how?

1) I don't think they "depend" on each other. The invariance group is the Galileo group for Newton's theory, the Poincaré group for Maxwell's theory. The second one is a Field theory, the first one not. The mass is a given quantity in the first one, a derived property of the fields in the second one. The first theory uses distant actions of the forces, the second one uses fields for propagating interaction, etc...

2) I think the sense of this is that Maxwell theory gives meaningful results only for extended bodies, that is, no point particles. If you try a delta-function charge-current density, at a certain point you'll find inconsistencies, like mass becoming infinitely negative, equation of motion of third order, etc.

 

[Misr]

Well,this looks sophisticated
we don't study all of this at school i just want a simple explanation..
I mean I want you to tell me that Maxwell theory compliments Newton's ...Law and why?
Thanks very much

 

[zomgineer]

Collectively, they are both classical field theories. Newton's laws describe gravitation fields among other things and Maxwell's equations describe electric and magnetic fields (and the relationship between electric and magnetic fields). If you combine the two, you can analyze a broad array of things that are big (not approaching atomic size).

Take a motor for example. It has real physical parts with inertia. There will be torque in the rotor that can be analyzed with Newton's laws. In addition, the motor will have magnetic fields, voltages, and currents. Newton+Maxwell can describe everything important that happens in the motor.

1-I read that Maxwell's theory depends on classical mechanics of Newton so how??and which law it depends upon?

I don't know exactly what they had in mind by saying that Maxwell's equations depend on Newton's laws but in a sense they do. We measure electromagnetic fields by the forces they create that act on mass. That's a Newton thing.

Interesting fact: Maxwell's equations led to the development of the Lorentz transformation which led to Einstein's theory of relativity which greatly improved upon Newton's laws (especially gravitation).