Are electromagnetic waves transverse or longitudinal?
If we swing a glass plate like a hand-held fan, then we cause an alternating air-current, that is, we cause longitudinal waves in the air. If we swing it pretty fast, then we cause sound waves at the same time (which are also longitudinal waves). If we now rub the glass plate with a woolen cloth, then the plate is electrified and if swing it again, we cause besides the air- and the sound-waves also electromagnetic waves, which are also longitudinal waves.
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I will jump for a moment to another question, to the one what an electric current is (for more details please see Mitko Gorgiev's answer to What is an electrical current?)
Electric current is an immaterial swirling wind through the electrical conductor. The immaterial magnetic wind through it is also spiral-shaped (i.e., it is not perpendicular to the conductor as the contemporary physics asserts). During the flow of direct current, both winds blow from the plus- to the minus-pole of the battery, the electric wind in counter-clockwise direction, whereas the magnetic wind in clockwise direction. These two fluxes are at angle of 90 degrees.
Here we have something very similar to the water swirl and its cavitation. When a propeller is turning underwater, then the swirling motion of the water is to one direction, while the motion of the cavities is at angle of 90° with respect to that of the water (drawing below). The faster the propeller is turning, the more extended is the water swirl and the more compacted is the cavities’ spiral.
The motion of the water corresponds to the motion of the electric wind; the motion of the cavities corresponds to the magnetic wind.
Please watch these two short YouTube videos (the first from 2:22):
Although the word “cavity” means something similar to “bubble”, still this cavitation is not a spiral from many bubbles, but a continuous hollow spiral, which is well noticeable in the second video. When the propeller stops turning, then this hollow spiral “dissolves” in separate cavities, i.e. in separate bubbles.
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The electric field of an electrified object, as well as the magnetic field of a magnetized object is twisted, something similar to a stranded wire (image below).
(image borrowed from ADKO)
It is not so hard to imagine the twisted field of a, let’s say, cylindrical magnet, but it is somewhat harder to imagine the twisted field of an electrified object. Here we have to recall on the principle of self-similarity. A beautiful example of this term in nature is the plant Romanesco broccoli. Considering it, we notice that the whole plant is a true reproduction of each of its parts.
Do you know the button-thread toy (also called thread spinner, button spinner, buzz saw toy)? The circular button has to have two holes symmetrically from the center through which the thread is threaded. We make the button spin by: 1) moving the hands closer and 2) by moving the hands farther apart. In both cases we apply force. In the first case we apply force to decelerate the button (minus), in the second case we apply force to accelerate the button (plus).
[ In the spinning button we have the same principle as in the EM-force element.
This principle of acting of the forces can be encountered in many places, even when we turn a bottle screw closure: the thumb presses into one, the forefinger into the opposite direction of the closure. ]
When we move an electrified object, then its twisted field moves together with it. If we move the object towards another (non-electrified) object, then the moving field evokes (/induces) an opposite field in the object. Now we have two objects: the moving and the still object. The EM-field between them becomes more twisted, just as the thread of the thread-spinner becomes more twisted when we move the hands closer. If we move the electrified object fast enough towards the other, then the friction between the EM-forces during the increasing twist is stronger, thus a tearing apart of the EM-“rope” can occur (which is visible and audible as a spark), just as when we move the hands fast enough, the friction between the double thread of the thread-spinner is stronger and a tearing apart of the thread can occur.
(please see Mitko Gorgiev's answer to What is electromagnetic induction?)
The lightning is also a tearing apart of the EM-”rope”.
[ Here a little digression: when a power line worker, sitting on a outrigger platform of a helicopter, approaches the power line, then he holds a long wand from a dielectric material (jokingly also called “magic wand”). Thus he advances the occurrence of the spark between the power line and the wand, which would otherwise has occurred between the power line and his body. Then he bonds himself to the power line. Why? Let’s say a sudden wind appears. It could blow the helicopter away from the power line together with the worker. In that case a spark will occur between the power line and the worker, because not only the fast approaching to the power line causes a spark, but also the fast moving away from it - just as the thread of the thread-spinner could tear apart when we move the hands farther apart.
By the bonding to the power line, the relative motion between the two objects is constrained.]
Please watch in this YouTube video how the worker uses the “magic wand” during the approaching and moving away from the cables (from 3:00 to 4:10)
Let’s consider an imagined experiment. We place vertically a very thin electrified glass plate, so thin as a membrane. There is a long piece of wire near the one side of the membrane. At the other end of the wire there is another non-electrified glass membrane (drawing below).
Sound waves hit the first membrane. As a result, the electrified membrane vibrates and produces EM-waves. These EM-waves propagate through the wire (it is actually an alternating current which oscillates just as the sound waves) and arrive at the other end of the wire. An oscillating EM-field appears around it which in turn electrifies the second membrane. This begins to vibrate in accord with the oscillating EM-field.
These vibrations reproduce the initial sound from the starting point of the experimental setup.
Here we have something similar to the kids telephone from two plastic cups connected via a tense thread.
P.S. This answer cannot be comprehensible to those who haven’t read the answers at the already given links.