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# Electromagnetic field

The electromagnetic field (EMF) is composed of two related vectorial fields, the electric field and the magnetic field. 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.

The electromagnetic field generates a force F on a charged particle, given by the Lorentz equation

where is the charge of the particle, v is its current velocity (expressed as a vector), and × is the cross product operator.

## 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

(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: .

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:

.

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.

The behaviour of electromagnetic fields can be described with Maxwell's equations, and their quantum basis by quantum electrodynamics.