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mysearch

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Apologises for the length of this post, but I am struggling to resolve some of the physical interpretations of Maxwell’s classical theory of electromagnetism. Therefore, I would appreciate any help on offer from those who have already resolved any of the issues raised. Many thanks.

As the questions are really asking for insights into the physical interpretation of Maxwell’s equations, rather than the maths, I am only providing a Wikipedia link to them:

http://en.wikipedia.org/wiki/Maxwell's_equations

So while I have generally worked through the derivation of Maxwell’s equations from the maths side, I am struggling with some of the physical interpretation of the interplay between electric and magnetic fields, especially when it comes to EM wave propagation. However, I have initially raised some issues for clarification against Maxwell 1 & 2 followed by Maxwell 3 & 4 before outlining the main questions concerning EM wave propagation:

**Some issues of interpretation with Maxwell [1] & [2]:**

*1) Maxwell [1] & [2] are time independent, therefore the charge [q] is considered stationary to some given observer. If [q] is stationary, no magnetic field (B) can be measured. So does the idea of a stationary permanent magnet or electromagnet need to be qualified in terms of Maxwell [4]?*

2) For instance, permanent magnets exist only as a special form of electromagnetism, i.e. the magnetic field is a result of moving charges that exist within the structure of the material?

3) What happens if a central stationary charge was surrounded by a neutralising shield, which could be switched on and off. When switched off, would an electric field propagate outwards at [c] without any implied magnetic field or would this propagation act as [dE/dt] with respect to Maxwell-4 and create an EM wave with a magnetic field component?

2) For instance, permanent magnets exist only as a special form of electromagnetism, i.e. the magnetic field is a result of moving charges that exist within the structure of the material?

3) What happens if a central stationary charge was surrounded by a neutralising shield, which could be switched on and off. When switched off, would an electric field propagate outwards at [c] without any implied magnetic field or would this propagation act as [dE/dt] with respect to Maxwell-4 and create an EM wave with a magnetic field component?

**Some issues of interpretation with Maxwell [3] and [4]:**

*4) Magnetic fields only exist by virtue of a moving charge, but the perception of the charge velocity [v] is relative to a given observer and therefore the magnetic field (B) is relative to the velocity of the observer and proportional to v*qSin(theta)?*

5) I am assuming the relative nature of the magnetic field does not apply within an EM wave because this wave always moves at [c] within all frames of reference?

6) While (E) and (B) are perpendicular to each other, these fields exist in a circular fashion in a plane that is perpendicular to the source in the context of Maxwell 3 or 4. I read that a current of one amp is equivalent to ~10^18 electrons. Therefore, I am not sure whether Maxwell-4 can be applied to a single electron moving at non-relativistic speeds in a vacuum. However, this model would seem to suggest that the electric field (E) would exist in all directions based on the inverse square law, while the magnetic field (B) would be proportional to qvSin(theta) implying a sine shaped magnetic field surrounding the moving charge at a given distance; this field would also be subject to the inverse square law. Presumably, this model reflects the E-M fields surrounding a physical charge [q] moving at a non-relativistic velocity [v] and not the EM wave emanating from the moving charge at velocity [c]?

5) I am assuming the relative nature of the magnetic field does not apply within an EM wave because this wave always moves at [c] within all frames of reference?

6) While (E) and (B) are perpendicular to each other, these fields exist in a circular fashion in a plane that is perpendicular to the source in the context of Maxwell 3 or 4. I read that a current of one amp is equivalent to ~10^18 electrons. Therefore, I am not sure whether Maxwell-4 can be applied to a single electron moving at non-relativistic speeds in a vacuum. However, this model would seem to suggest that the electric field (E) would exist in all directions based on the inverse square law, while the magnetic field (B) would be proportional to qvSin(theta) implying a sine shaped magnetic field surrounding the moving charge at a given distance; this field would also be subject to the inverse square law. Presumably, this model reflects the E-M fields surrounding a physical charge [q] moving at a non-relativistic velocity [v] and not the EM wave emanating from the moving charge at velocity [c]?

**The EM wave equation of motion:**http://physics.info/em-waves/

The maths presented in this link seems as clear a derivation of the EM wave equation as I could find, although I prefer to substitute E=E0 Sin(ky-wt) and B=B0 Sin(kz-wt) to represent the perpendicular plane waves for E & M. I liked the approach as it directly shows the development of the EM wave equation from Maxwell’s equations. However:

*8) Should I interpret the picture of an EM wave, as illustrated in the link below, in terms of the Lorentz force equation. For example, as an EM wave passes a point in space occupied by a unit charge, this charge would be subject to the perpendicular component forces defined by F=q(E+vxB)? http://www.montalk.net/emavec/EMtransverse.jpg*

9) On the basis that the charge density [I,J] are zero in Maxwell [1] and [4] what is the classical model for the source of an EM wave, i.e. Maxwell’s equation predates the idea of a photon or even the atomic model, so was the classical source of an EM wave always assumed to be an oscillating charge?

10) Standard texts suggest the energy associated with both the electric and magnetic field is proportional to the square of the electric field (E). This seems analogous to a mechanical wave where energy is always proportional to the amplitude squared. Is there a connection between these models and when was it subsequently tied to Planck’s equation Energy=hf?

11) If I assume the EM wave is started by an oscillating charge in free space, which quickly stops, should I also assume that the energy in the EM wave continues to propagate as a finite pulse without any loss forever, i.e. energy conservation applies in the absence of any loss mechanism for EM waves in vacuum?

12) In a mechanical wave, the total energy at any point of the wave can always be approximated as the sum of the potential and kinetic energy. However, because the E and B components of the EM wave are in phase, there seems to be points where E and B are both zero. Is there is some minimum ‘quanta’ of an EM wave over which the energy has to be aggregated, which also leads to the idea of some minimum quanta of momentum = E/c?

13) How did classical physics of Maxwell’s equation explain 12) prior to the idea of photon quanta?

9) On the basis that the charge density [I,J] are zero in Maxwell [1] and [4] what is the classical model for the source of an EM wave, i.e. Maxwell’s equation predates the idea of a photon or even the atomic model, so was the classical source of an EM wave always assumed to be an oscillating charge?

10) Standard texts suggest the energy associated with both the electric and magnetic field is proportional to the square of the electric field (E). This seems analogous to a mechanical wave where energy is always proportional to the amplitude squared. Is there a connection between these models and when was it subsequently tied to Planck’s equation Energy=hf?

11) If I assume the EM wave is started by an oscillating charge in free space, which quickly stops, should I also assume that the energy in the EM wave continues to propagate as a finite pulse without any loss forever, i.e. energy conservation applies in the absence of any loss mechanism for EM waves in vacuum?

12) In a mechanical wave, the total energy at any point of the wave can always be approximated as the sum of the potential and kinetic energy. However, because the E and B components of the EM wave are in phase, there seems to be points where E and B are both zero. Is there is some minimum ‘quanta’ of an EM wave over which the energy has to be aggregated, which also leads to the idea of some minimum quanta of momentum = E/c?

13) How did classical physics of Maxwell’s equation explain 12) prior to the idea of photon quanta?