Capacitor Two conductors carrying charges of equal magnitude but opposite sign form a capacitor. +Q -Q A parallel plate capacitor is a particularly common type: +Q-Q Capacitors have a voltage across them

Capacitor: Field Lines +q -q Perfect parallel plate capacitors have a uniform field. And of course a potential difference

Capacitors and Charge Capacitors store charge Capacitance is measure of how well it stores charge Capacitance is a constant for a given capacitor. Farad (F) is C/V, the unit of capacitance Typical capacitances are in  F or pF ranges.

Capacitors and Charge Capacitance is a constant for a given capacitor. The voltage (i.e. potential difference) used is this equation is positive. C depends only on the geometry of the capacitor! Note: the material doesn’t matter (except in between the plates} If I change the voltage (for a given geometry), I change the charge. If the charge changes, than the voltage must have changed

Finding Capacitance a b +Q+Q-Q-Q So we need to find the field the find the voltage (use Gauss law, with the sphere as the gaussian surface )

Finding Capacitance a b +Q+Q-Q-Q

Finding Capacitance: isolated sphere a b +Q+Q-Q-Q a b +Q+Q-Q-Q The isolated sphere is the limit as b-> infinity of the concentric spheres

A Parallel Plate Capacitor d area A Dielectric constant 