I have not thought deeply about this, but feel that the answer may lie in thinking of the circuit as a fully 3D object.
Between the capacitor plates, sure that's where E and B are pointing, but outside the plates you have a fringing field and E has a radial component, which must mean S must...
It was not intended that the statement add to the conventional description. It was intended to explain how the analogy remained applicable. We are in a teaching forum, after all.
I think the analogy still works. Why does a ball held up high have more energy than a ball resting on the ground? Why does that extra energy get converted when it moves towards the ground?
Same as an electron moving between two points with a voltage.
The induced electric field is entirely separate from that which is created by the battery. They are added together. The battery drives a current through the circuit. If you move a magnet near the circuit, then you will see an additional "EMF" in the circuit that can contribute to the total...
If the wire is superconducting then it is not Ohmic and you can't use V = IR.
In reality, if you were to apply that voltage across a superconducting wire, you'd probably melt the voltage source as that still contributes its own internal resistance to the circuit.
Think of "time" as a continuous, ordered set of moments. "Now" is one of those moments, though which particular moment it happens to be depends on when you say the word.
Think also of "space" as an ordered set of places. "Here" is one of those places, but the exact one referred to depends on...
You didn't specify ions in your original question. That is important information (more of which is needed).
Ions in a gas move in all directions, unlike in a mass spectrometer. What is the reason for an increase in concentration in a particular region? What breaks the symmetry?
We are not talking about excess free charge placed on a conductor (like a capacitor plate) which will move to the outside, the charge in a neutral (but conductive) wire is simply due to the charge carriers, and is completely neutralised over macroscopic scales by the positive ionic lattice. So...
A vibration mode describes a type of vibration an object can undergo. Normal modes are the set of orthogonal modes, I.e. set of modes from which all possible vibrations can be expressed.
Each normal mode occurs with a particular resonant or natural frequency.
The molecules cannot dissappear but they can change phase under sufficient pressure. THe exact conditions required to cause a phase change will depend on the gas and are summarised in a phase diagram.