# Electromagnetic field

In the physics of electromagnetism, an electromagnetic field is a field composed of two related vector fields: the electric field and the magnetic field. When referred to as the electromagnetic field, the field is imagined to encompass all of space; typically an electromagnetic field is considered to be limited to a local area around an object in space.

The vectors (E and B) that characterize the field each have a value defined at every point of space and time. If only the electric field (E) is non-zero, and is constant in time, the field is said to be an electrostatic field. E and B (the magnetic field) 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 incompressible fluids which permeate space. In the absence of charges these fluids would be at rest, so that their velocity fields would be zero. Since both fluids are incompressible, their densities do not change: it is not possible to compress magnetic or electric fluid into a smaller space.

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

$\displaystyle v = {\epsilon \over 4 \pi r^2}$

(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: $\displaystyle 4 \pi r^2 \cdot v = \epsilon$ .

Magnetic liquid, on the other hand, has no sources or sinks: there are no magnetic charges that could pour out or suck up magnetic fluid. 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 indirectly causes 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.

To summarise, 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.

The opposite signs of acceleration 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:

$\displaystyle \Delta E \rightarrow + \Delta B$
$\displaystyle - \Delta E \leftarrow + \Delta B$ .

If there were a positive feedback loop, the result might be similar to the high pitched resonant effect produced by a microphone too close to its speaker. 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 and conservation of energy being what they are, an initial disturbance (acceleration) of the electric fluid will cause a feedback loop that, 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 is flawed, in 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 $\displaystyle \mathbf{F} = q \mathbf{E}$ , a force that is independent of the velocity of the particle. This means that the particle will accelerate continually in the direction of the field. If the field were the velocity field of a fluid then the fluid would cause the object to accelerate continually in the direction of the fluid's motion, to the point that the object's speed becomes paradoxically far greater than that of the fluid is in which it is immersed.

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; 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 proposition that the motion of the earth relative to the aether might be detectable (i.e. through an "aether wind") was disproven by the Michelson-Morley experiment, whereupon it was argued that the experiment had disproved the very existence of the aether. This opinion prevailed, but remains disputed by some who equate the classical concept of the aether with the modern notion of a quantum electrodynamic fluid. (The disputants argue that proving that the earth does not travel through an "aether wind" is no more nor less significant than proving that the earth does not travel through its own gravitational or magnetic fields.) The necessity of an aether was seen to have vanished when it was replaced by Einstein's theory of relativity.

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

$\displaystyle \mathbf{F} = q \mathbf{E}.$

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 [1].)

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 transverse 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? Electromagnetic (E-M) waves are the undulatory movements 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 a charged particle is in inertial motion, then the electrostatic field is joined by a magnetostatic field. This 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:

• charges generate fields
• the fields interact with each other
• fields act upon charges
• Lorentz force: force due to electromagnetic field
• electric force: same direction as electric field
• magnetic force: perpendicular both to magnetic field and to velocity of charge ($\displaystyle \star$ )
• charges move

Phenomena in the list are marked with a star ($\displaystyle \star$ ) 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.