I am not sure what you are asking.
Hand waving follows; look up Maxwell's equations. There are also numerous online tutorials with pictures and much better explanations but hopefully this will get you started.
When you pass current through a wire, a magnetic field is automatically generated at right angles to the current flow. That is the often-mentioned EM (electromagnetic) field. Conventional speakers use a coil of wire around a permanent magnet. Many of us made an electromagnet from a nail and coil of wire, or made a little electric motor. Wrap the wire around a magnet, and as the signal current goes back and forth (reverse polarity) it will create a magnetic force that works with and against the magnet. Send the current one way, and the magnetic fields attract; the other way, and they oppose, so as the signal varies you get "pushing" and "pulling" forces. Attach the wire (voice coil) to a cone of some material, and then when you apply signal current (e.g. from your amplifier) the magnetic force pushes against the permanent magnet and moves the cone. The cone in turn creates vibrations in the air -- sound.
Planer-dynamic speakers like Magnepans basically take the voice coil and turn it into long strips of wire going up and down a large lightweight moving panel (the cone gets flattened and spread out). The magnet becomes strips of magnets on a fixed panel behind (usually) the moving panel. Now, when you apply signal to the wires, again a magnetic field is created that pushes against the strips of magnets, and the whole panel moves back and forth. This may provide lower distortion, since the entire panel ("cone") area is driven, but also much less movement since the moving panel has to be close to the fixed panel for the signal current to generate enough magnetic field to push against the magnets and move the panel.
Electrostatic speakers (ESLs) like Martin Logans use a different scheme entirely. In their case, two voltage fields are generated; a DC (static, non-moving) field on a light, thin conductive diaphragm (panel). Panels on either side are driven (through a step-up transformer to create the high voltage required) by the audio signal. Now there are no magnets, but opposite charges (voltages) attract, and similar charges repel, so again there are forces that move the diaphragm back and forth. Electrical voltage fields instead of magnetic fields, but the same general idea. Again the light diaphragm is driven over its entire area, and covers essentially the entire audio band with a single driver, so can have lower distortion but less dynamic range than a conventional driver.
Planar speakers (Maggies or ESLs) radiate equally out the front and rear so the back wave can cause a more "spacious" sound but also lead to cancellations when the back wave combines with the front, causing ripples in the frequency response (comb filter effects). They do not radiate much to the sounds or top/bottom so have less problem with wall or ceiling/floor reflections. Conventional speakers radiate more-or-less in all directions so in general "fill the room" more but are also more sensitive to reflections from walls, ceiling, and floor that can cause frequency ripples in the sound. They do tend to play louder and provide more bass than planar speakers.
HTH - Don