Capacitance


The capacitance CC of a system of two conductors is the constant of proportionality between their charges and their electric potential. For two conductors with charges QQ and Q-Q respectively, their capacitance is

C=QV=QV+V[F][CV]C=\frac{Q}{V}=\frac{Q}{V_{+}-V_{-}} \qquad [\text{F}]\equiv\left[ \frac{\text{C}}{\text{V}} \right]

where V+V_{+} is the potential of the positive conductor and VV_{-} is that of the negative one. It is measured in Farads. Common amounts are measured in either microfarads (106 F10^{-6}\text{ F}) or picofarads (1012 F10^{-12}\text{ F}). Capacitance is a purely geometric quantity and depends on the shape, size and separation of the conductors. It is inherently positive, as the charge is that of the positive conductor and the potential is the positive potential minus the negative one.

It's possible to talk about the capacitance of a single conductor by choosing the second (negative) conductor to be a spherical shell of infinite radius centered around the positive capacitor. In this case, the negative potential is just zero (if the point of reference is picked at infinity). For instance, the capacitance of a sphere of radius RR is C=4πε0RC=4\pi \varepsilon_{0}R.