| Those are two very different things (Ohm's Law and Capacitance). Capacitance is basically the relation between electric field and charge, whereas inductance is the relation between magnetic fields and currents. Those follow from fundamental equations, if you want a calculus intensive derivation from the "first principles" of Maxwell's Laws. Someone on this thread mentioned Griffiths, which is a good text, it's what I used in E&M undergrad. Wangsness has a good E&M text too I liked. Ohm's Law is a macroscopic statistical mechanical Law that happens in bulk. It can be derived from even some of the simplest electron models (eg the very simplistic Druude Model). Where it can be shown that the current density through a chunk of material is proportional to the applied electric field.
https://en.m.wikipedia.org/wiki/Drude_model But it breaks down in smaller systems, where statistical averages don't hold (for example ballistic conductance in a nanowire). Or other systems when quantum mechanical effects will dominate (eg bandgap non-linearities of a PN Junction or Quantum Well, or how the bandgap of a semiconductor causes an increase of resistance at lower temperatures as opposed to decrease of resistance for metals). I used to have a nice presentation of the latter on my old uni website called A Quick and Dirty Preview to Solid State Physics, but alas they disabled my old account after nearly a decade past graduatiOn. (Had to make the webpage for a class early in grad school, and it was linked by many other solid state physics classes interestingly). |