Capacitance and Geometry Great mysteries of the universe elucidated by your good friend Gauss…

Capacitance Capacitors are charge-storage devices Capacitance, C, is a measure of the ability to store charge You have to do work to store charge on a capacitor Energy is stored in the e-field between the cap’s electrodes 1 C/volt = 1 farad [F]

Parallel-plate capacitors Consider two plates of opposite charge separated by a gap d and carrying a charge density s The field between the plates is and the field beyond them is zero.

Parallel-plate capacitors Recall that Since and the potential difference across this capacitor is Given the definition of capacitance the capacitance of this geometry is

Cylindrical capacitors Inner cylinder carries a charge density of +l while the outer carries -l At any arbitrary location so therefore

Cylindrical capacitors Since for this geometry,

Spherical shells Consider an inner shell charged at +Q and an outer shell charged at -Q At any arbitrary location and therefore and for this geometry

Isolated conductors as capacitors Think of the 2nd electrode as infinitely far away At the surface, At the 2nd electrode V=0, so for this geometry