I was going over my notes for an introductory course to electricity and magnetism and was intrigued by something I don't have an answer to. I remember my professor mentioning, to the best I can remember, that electric current is actually not the flow of electrons but the propagation of the electric field. My question is, how does the field "know" in which direction to travel, or even what to travel along? The electrons just move from atom to atom as they feel a force due to the potential difference (if I have it right). But what about the field? Thanks to all in advance.
You're right. The field will indeed extend outside the electric conductor as well. However, since there are very few electrons affected outside the conductor, the field strength will quickly drop outside the conductor. However, inside the conductor, where the field does move many additional electrons, those movements will contribute to the field strength.
The field strength is not directly related to its speed, though.
Electric current, by definition, is a flow of charged particles.
When someone says it is the propagation of the electric field, usually he means the following:
The velocity of the electrons in the wires is very slow (few cm/s if I remember it right), but when one turn on the light he doesn't see any delay. The lamp starts lighting when the electrons start move inside it, not when the electrons come from the light switch to it. The electric field travels through the wires and make the electrons move everywhere.
When one connects a wire to the source the electric field exists only at the start of the wire. This field makes electrons move and changes their density. This perturbation produces electric field in the area around and moves the electrons in the nearby part of the wire.
This perturbation spreads very fast almost with the velocity of light.
This process can be compared to a shock wave. The wind is, by definition, a flow of the molecules of the air. But the difference of pressure (the shock wave) that makes them move can spread even faster than sound.
There's an old and clichéd but actually pretty good analogy for understanding electric circuits, and that's to think of the circuit as water plowing through pipes.
If you have a pipe full of water, and you turn on the tap at one end, water immediately starts flowing out of the other end. Well not quite immediately: when you turn on the tap you raise the pressure (in this analogy pressure = voltage) and generate a pressure wave that travels along the pipe. When the pressure wave reaches the far end of the pipe it causes the water to start flowing.
This is analgous to Maksim's comment "This process can be compared to a shock wave", and in an electrical circuit the "voltage wave" travels at near the speed of light. In the water pipe the wave travles at the speed of sound in water. In both cases it doesn't matter how fast the water/electrons are travelling, it's the speed of the wave that matters.