The physical cause is the resistor and capacitor between the two wires. Two adjacent points on either wire A or B are separated by a very small resistance. But the two wires are separated by whatever the value of R is. Via Ohm's Law, the voltage drop across R can be calculated.A voltmeter connected to two different points on wire A will read very close to zero potential difference the whole time; but the same meter connected from wire A to wire B will reveal a significant potential difference at the start of the discharge period. What is the physical cause of this potential difference?
No, there mustn't. You are locked into an idea that is incorrect. If you can't get passed that, nothing here will help. For a simple DC circuit, most of the "water analogy" applies. A wire is a garden hose ***already full of water*** (electrons). When you open the faucet, more water (electrons) go into one end of the hose, and almost immediately water/electrons come out the other end of the hose. OK, a major flaw in the water analogy is that a complete circuit is not needed for flow, but I hope you see the concept here. So electrons are physically moving through the hose. There are two consequences, already pointed out: heating caused by resistance, and deflection caused by the electric and magnetic fields.There must be something different about wires A and B during the period in question. What is it?
NOTE (a big note): the electrons in the wires in a DC circuit do not move at the speed of light, or anything near it. In the hose analogy, note that water starts coming out the far end of the hose almost immediately, even though the water entering the hose will take many seconds to reach the end. This is the difference between the way electromagnetic energy moves down a wire, and the way electrons move through it. Think of a ceiling light in a room, controlled by a wall switch, and powered by DC instead of AC. Flip the switch, light comes on too fast to perceive any delay. But electrons at the switch contact could take 30 minutes (not a typo) to reach the light bulb.