Well I was learning transmission but I got a bit confused when I came to coaxial cables transmission at radio frequency.
What I am lost is how the waves are propagating in the cable, I was thinking that AC current just flows through the conductor just like a normal 2 wire system to the antenna. But the electric fields are not in the direction of the current but is in only between the two conductors (inside, and outside).
Why is this? I am so confused
The thing to realize is that all electrical phenomena are governed by Maxwell's equations, which describe the relationship between electrical and magnetic fields and how they affect each other over time.
However, in many cases, we can analyze circuits using what's called the lumped circuit approximation. This is a set of rules that can be derived from Maxwell's equations. These rules apply when the circuit is small enough that speed-of-light delays from one side of the circuit to the other are insignificant. Kirchoff's voltage and current rules are the main tools for analyzing circuits in the lumped circuit approximation. I think these cases are what you're talking about when you say you're familiar with "a normal 2 wire system" where "ac current just flows through the conductor".
We start talking about transmission lines when we have a conductor (and return path) that are long enough that speed of light matters. To analyze transmission line propagation, we use a different not-quite-so-simple simplification of Maxwell's equations called the telegrapher's equations. The solutions to the telegrapher's equations describe the propagation of signals on transmission lines. A full description and solution of the telegrapher's equations is more than I can write here, but you can read more about them on Wikipedia, for example.
The gist of it is, as you've probably learned, energy is transferred back and forth between electric and magnetic fields. The important electric field is the one created by the potential difference between the conductors, which extends through the dielectric medium. Similarly, the important magnetic field is created by the currents in the conductors, but the field is actually found in the dielectric. In the telegrapher's equations the electric field effect is represented by a "distributed" capacitance and the magnetic field by an "distributed" inductance, which lead to our typical characterization of transmission lines by capacitance and inductance per unit length, which combine to give the characteristic impedance.
Assuming you understand how transmission lines work in general, coaxial cables are really no different. The only thing that is unique about them is their self-shielding property.
Since the outer conductor completely surrounds the inner conductor, the electric field arising from the potential difference between them is completely contained. The only field that can exist outside the outer conductor could only arise from a voltage difference between that conductor and some other reference.
There is a magnetic field associated with each of the conductors, but since the currents are equal and are flowing in opposite directions, and the inner wire and the outer cylinder share a common axis, the two fields in the space outside the outer conductor cancel exactly.
Does this address your confusion?
... coaxial cables transmission at radio frequency. ... how the waves are propagating in the cable, I was thinking that AC current just flows through the conductor just like a normal 2 wire system to the antenna.
Yes, electrical charges flow through the 2 conductors of a coax cable, exactly the same as the electrical charges flow through the 2 conductors of a 2 wire system.
But the electric fields are not in the direction of the current but is in only between the two conductors (inside, and outside).
Yes, the electric field is (mostly) between the two conductors of a 2 wire system, just like the electric field is (mostly) between the two conductors of a coax cable.
Yes, the flow of electromagnetic energy (the Poynting field) is, as always, the cross product of the magnetic field and the electic field, no matter if we use a coax cable or a pair of wires to guide that energy from one place to another. See http://amasci.com/elect/poynt/poynt.html .
Since the electric field is nearly zero inside all metallic conductor, nearly zero electromagnetic energy flows through any metallic conductor, including the conductors in a coax cable and the conductors of twisted pairs of wires.
