I'm reading through my E&M textbook (Physics for Scientists and Engineers 3rd edition, Knight) and watching as many lectures on YouTube (Shankar, Pomerantz, Lewin, etc) to prepare for next quarter. I have one question as I don't want to learn a wrong concept.
I've noticed when you charge a capacitor with a constant current you get a voltage slope. After watching Carver Mead talk on G4g, I later saw that for an inductor $V = L \frac{dI}{dt}$. Which looks strikingly similar to the equation I've learned up to this point for capacitors, $I = C \frac{dV}{dt}$. That's weird.
If you charge a capacitor with a constant current you get a slope of the voltage, then do you get the slope of the current if you charge an inductor at a constant voltage?
Are these mirrored concepts?
If this is the case it makes sense to me. So much of an electrons motion seems dependent on it's path or type of path. At least from what I've learned to this point. Conductors and inductors seem to be taking advantage of the same rules for different outcomes.