What are Electric & Magnetic Fields composed of?

[Intropersona]

Field of what exactly?

Sounds is vibrations in air molecules.

Electromagnetic waves are vibrations in fields of what? Where are these fields existing?

Wiki states that fields are "A field is a physical quantity that has a value for each point in space and time."

Where is the physical quantity of E & M fields?

This wiki description really seems like a beating around the bush at conferring what exactly these things are in their essence.

 

[Delta2]

Well you are *initially* right on this problem. To address this problem physicists initially developed the theory of aether http://en.wikipedia.org/wiki/Aether_theories. But later they dismiss this theory and just accepted that the EM field (as well as the gravitational field) is a property of spacetime, that is simply at any point (x,y,z,t) of space time we can assign a value f(x,y,z,t) for any field of interest (let it be electric, magnetic, gravitational, weak or strong nuclear).

 

[Drakkith]

Electromagnetic waves are vibrations in fields of what?

They aren't vibrations at all. They are a cyclic change in the direction and magnitude of the electric and magnetic field vectors. The field vectors are vector quantities that specify the direction and magnitude of the force felt by a charged particle in an EM field. An EM wave is these vectors changing, cycling over time in a way that is described by a wave equation.

Where are these fields existing?

They exist everywhere.

Where is the physical quantity of E & M fields?

Per wiki: A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.

The 'physical quantity' in this case is the vectors I mentioned. You can measure their magnitude and direction, making them physical quantities.