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

2. 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]

3. 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.

4. 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

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

6. Cylindrical capacitors
Since
for this geometry,

7. 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

8. 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