Paper I showed the one behavior: a capacitor reports change, never state. Now watch that single trick do three jobs — strip a bias, choose which changes pass, and leap a gap with no wire at all. Same law each time.
The most common capacitor in all of communications does exactly one thing: it sits in series with a signal and refuses to pass the part that isn't moving. A microphone's output, a radio stage, an audio line — they often ride on a steady DC voltage that's just bias, not information. Put a capacitor in the path and the bias is blocked while the wiggle sails through. It falls straight out of Paper I: the steady part has zero slope, so the cap is blind to it; only the changing part survives.
The bias is the state. The wiggle is the message. The capacitor passes only the message — because it was only ever a change-detector.
If a capacitor passes change, the obvious next question is: which change? Pair it with a resistor and the answer becomes tunable. Fast wiggles (high frequency) and slow drifts (low frequency) get treated differently, and a single number sets the dividing line — the cutoff frequency, fc = 1 / (2πRC). Below it one way, above it the other.
Wire the cap one way and you get a high-pass filter — fast changes through, slow drift rejected (this is the coupling cap, generalized). Flip it and you get a low-pass — slow changes through, fast jitter smoothed away. Selective listening, built from one cap and one resistor.
Slide the test tone across the cutoff and watch the gain hand it through or turn it away. The corner isn't a wall — it's a smooth 45°-per-decade slope — which is itself a consequence of i = C·dv/dt integrated against a resistor.
Here is the one that matters, the rigorous version of every gap you've ever wondered about. Two conductors near each other are a capacitor — you don't have to build one. So when the voltage on the first plate changes, a current flows in the second plate across the empty gap — even though no charge ever crosses. The plates never touch. The message arrives anyway.
What carries it is the changing electric field in the gap. James Clerk Maxwell named this displacement current in 1861 — and it's not a metaphor for current, it's a term he had to add to make his equations consistent, the missing piece that predicted electromagnetic waves and therefore radio, light, all of it. And the punchline, checked to the digit: displacement current is ε₀·A·dE/dt, which equals C·dv/dt exactly. The gap-crossing is the same law as Paper I.
No charge crosses the gap. The changing field carries the current — and that is real Maxwell physics, not an analogy. The wire was never necessary; the change was.
Five instruments, one equation. The slab held a state; the differentiator proved current follows the slope; the coupling cap stripped a bias; the filter chose which changes pass; and the gap carried a message across empty space with no wire. Every one was i = C·dv/dt pointed at a different job — because a capacitor was always a communicator, and the thing it communicates is, only and exactly, change.
Where it could go next, if you want a Paper III: the cap as memory (DRAM, sample-and-hold — storing a change long enough to read it), or the cap as sensor (touch, proximity, microphones — the world changing the field), or up into real-world non-idealities (ESR, dielectric absorption — where the ideal model finally has to pay its debts).