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.

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.

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However, the force of an electric field on a charged particle is 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.

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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.

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