Electromagnetic field

From Academic Kids

In the physics of electromagnetism, the electromagnetic field is a field composed of two related vectorial fields —the electric field and the magnetic field. When referred to as "the" electromagnetic field, encompassing all of space, whereas typically such a field is limited to a local area, based around an object in space.

This means that the vectors (E and B) that characterize the field each have a value defined at each point of space and time. If only E, the electric field, is nonzero and is constant in time, the field is said to be an electrostatic field. E and B are linked by Maxwell's equations.

Electromagnetic fields can be explained with a quantum basis by quantum electrodynamics.


Behaviour of the electromagnetic field

(A hydrodynamic interpretation)

The electric and magnetic vector fields can be thought of as being the velocities of a pair of fluids which permeate space. In the absence of charges these fluids would be at rest, so that their velocity fields would be zero.

Electric charges act either as sources or sinks of the electric fluid. An electron is constantly absorbing electric fluid around it at some rate, call it ε. Protons are the reverse: they constantly pour electric "liquid" towards the surrounding space at rate ε, so liquid moves away from the proton with speed

<math> v = {\epsilon \over 4 \pi r^2} <math>

(where r is distance of the fluid away from the proton) so that the total flux of liquid going through any (imaginary) sphere which contains that proton is the area of the sphere times the speed of the fluid flowing through it: <math> 4 \pi r^2 \cdot v = \epsilon <math>.

Magnetic liquid, on the other hand, has no sources or sinks: nothing can pour out or suck up magnetic fluid. Magnetic fluid is incompressible, which means that its density does not change: it is not possible to compress a lot of magnetic fluid into a smaller space, or to squash it out of a given volume. (Electric fluid is also incompressible, but it has sources and sinks.) If magnetic fluid is standing still, it can be stirred up, making it move in closed circles and closed loops (see vortical motion).

For the magnetic fluid to keep moving in the same loop, though, some force has to keep stirring it up: otherwise the energy of its circular motion will dissipate and the magnetic fluid will stop moving and will return to rest.

If electric fluid starts to accelerate in a certain direction, it will cause a vortex of magnetic fluid to move in circles around the direction in which the electric fluid is accelerating (according to the right hand rule). As soon as the electric fluid stops accelerating, the vortex of magnetic fluid vanishes.

Notice that: electric fluid will not accelerate spontaneously. Something has to force it to accelerate. This same thing then causes (indirectly) the magnetic vortex to be stirred up. A magnetic vortex will not arise spontaneously.

Finally, if magnetic fluid accelerates in a certain direction, it causes electric fluid to move in a vortex which circles around the direction of acceleration in the direction opposite to the right hand rule.

Summarily: an acceleration of the electric fluid causes a positive vortex of magnetic "liquid" to move around it, but an acceleration of the magnetic liquid causes a negative vortex of electric liquid to flow around it.

Why the opposite signs? The opposite signs create a negative feedback loop (see Lenz's law.) An acceleration of electric fluid causes a positive magnetic vortex. This means that the magnetic fluid has been accelerated to produce this circular flow. But this causes a negative vortex of electric fluid around the magnetic vortex. This reactive vortical acceleration of electric fluid is in the direction opposite of the original acceleration of electric fluid: hence a negative feedback loop:

<math> \Delta E \rightarrow + \Delta B <math>
<math> - \Delta E \leftarrow + \Delta B <math>.

If there were a positive feedback loop, the result would be (presumably) similar to the effect produced by a microphone too close to its speaker: a deafening high pitched resonant noise. The positive feedback would cause the original acceleration of electric fluid to amplify itself continually, while at the same time the vortices around it would amplify as well: an explosive maelstrom of movement of electromagnetic fluid. Fortunately, the laws of electromagnetism being what they are, an initial disturbance (acceleration) of the electric fluid will cause feedback loop which, being negative, will tend to extinguish itself at its source but which will propagate outwards in what is called an electromagnetic wave.

Flaw in the velocity field interpretation

The fluid analogy does not work in this sense: that objects immersed in a moving fluid (e.g. a river) tend to be pushed by that fluid in such a way that the velocity of the object aligns with the velocity of the fluid. Once the velocities are aligned, the fluid's motion should vanish from the object's point of view.

However, the force of an electric field on a charged particle is <math> \mathbf{F} = q \mathbf{E} <math>, and this force is independent of the velocity of the particle, which means that the particle will accelerate continually in the direction of the field. If the field is the velocity field of a fluid then the fluid would be causing the object to accelerate continually in the direction of the fluid's motion, to the point that the object's speed becomes far greater than that of the fluid is in which it is immersed. This is paradoxical.

From the continually accelerating object's point of view (see principle of relativity), if its speed has already surpassed the speed of the fluid, then the fluid is moving backwards, so the field should be pointing in the direction opposite to the direction in which the object keeps accelerating. This means that the object should stop accelerating and begin decelerating, until its speed aligns with the speed of the electric fluid.

The field as a stream of moving photons

An alternative interpretation would be that the field is not actually a velocity field, but a flux density field of photonic fluid, which is constantly moving at the same speed: the speed of light, independent of the speed of the observer (the charged object). Photonic fluid never changes speed but can change net direction and the intensity of its net movement in that direction.

The velocity field interpretation is related to the hypothesis of a luminiferous aether through which electromagnetic waves would propagate. The existence of the aether was disproved by the Michelson-Morley experiment and the necessity of having an aether vanished when it was replaced by Einstein's theory of relativity.

According to special relativity, the Lorentz force equation reduces to the equation

<math> \mathbf{F} = q \mathbf{E}. <math>

The magnetic field becomes a relativistic by-product of the electric field. I.e. Lorentz transformations cause magnetic fields to be induced from electric fields, and vice versa. So the photonic fluid describes the electric field, and relativistic effects account for the derivative magnetic field. (This can be derived by applying a Lorentz transformation to a simplified version of Maxwell's equations, and it is mentioned by Einstein in his paper On The Electrodynamics Of Moving Bodies.)

The speed of light is invariant under a Lorentz transformation, but the velocity of light is changed. The component of the velocity of light parallel to the boost is left unchanged, but the transversal component is rotated: it is accelerated in a direction parallel to the boost. The addition of special relativity allows the combination of the electric and magnetic fields into a single tensor field. The tensor character of this combined electromagnetic field implies that the field is anisotropic with respect to the velocity of the charged particle on which it produces a force: the Lorentz force varies with the velocity of the charged particle.

Light and electromagnetic waves

Electrically charged particles are constantly emitting (or absorbing) photonic fluid, which is more commonly known as light. So how is light related to electromagnetic waves? E-M waves are undulatory movement patterns of light which can always be observed to be emitted by electric charges undergoing acceleration.

If a charged particle is at rest, then it does not emit electromagnetic waves. Instead, it is surrounded by an electrostatic field. If the charged particle is in inertial motion, then the electrostatic field is joined by a magnetostatic field. These pair of static fields produce a movement of electromagnetic energy (i.e. a field of non-zero Poynting vectors), which is similar to an electromagnetic wave, except that the fields are not oscillating.

E-M waves are propagating, expanding, harmonic, oscillating, accelerations of the photonic fluid. Since the photonic fluid itself moves at the speed of light (by definition), then E-M waves can move no faster than the speed of light. E-M waves move at a speed close to the speed of light, depending on the medium through which they move (e.g. faster in air than through water, and faster through water than through a glass lens).

The electromagnetic field as a feedback loop

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:

Phenomena in the list are marked with a star (<math>\star<math>) if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz transformations to electric fields and static charges. This means that the magnetic field ends up being (conceptually) reduced to an appendage of the electric field, i.e. something which interacts with reality only indirectly through the electric field.

See also

External links

es:Campo electromagnético fr:Champ électromagnétique it:Campo elettromagnetico nl:Elektromagnetisch veld ja:電磁場 pl:Pole elektromagnetyczne sv:Elektromagnetiskt fält vi:Trường điện từ zh:电磁场


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