How to Find Capacitance for Spherical and Cylindrical Capacitors

There are three shapes of capacitors in practice: parallel-plate, spherical and cylindrical. Conveniently, these are the three shapes we have for Gauss's law applications. We will use Gauss's law to find the E-field in the capacitors, then integrate the fields to get the potential difference across the capacitor, and then use our definition of capacitance, C = Q / V, to get the capacitance expressions. Let's take a look at two of the three, spherical and cylindrical capacitors.