Capacitance (Chapter 26) Capacitance – the property of a conductor or set of conductors and insulators to store electric charge Capacitor – an electronic component that has the ability to store charge Definition Calculating Capacitance Dielectrics and Dielectric Constant

Definition: Capacitance C of two conductors with equal but opposite charges V = potential difference created when charge +Q is on one conductor, and –Q is on the other. Unit: Typically ranges from 1μF = 10-6 F and 1pF = 10-12 F 1 F is a LOT of stored charge !!!

Finding C for Symmetrical Charges 1) Find the electric field as a function of r using Gauss’s Law. 2) Choose a path along a field line: the potential change with each small change dr in distance is dV = - E(r)dr 3) Integrate from start to end of field line to find the potential difference. 4) C=Q/V

Example 1: Parallel Plates area A, separation d d +Q -Q Surface charge densities: Recall … (between plates) (uniform ) Hence, C depends only on the geometry of the plates

Quiz: d +Q -Q As the plates are moved apart, which of the following will increase, decrease, or stay the same? Electric field between the plates Electric potential difference between the plates Capacitance of the plates

Example 2: Sphere What is the capacitance of an isolated spherical conductor of radius R and charge Q?

Example 3: Concentric Spheres Derive: R1 R2 -Q +Q

Examples: Find capacitances of… 2 sheets of foil, 25 cm x 40 cm, 1 mm apart (in air.) The earth and the ionosphere (height: 100 km) as a pair of concentric spheres.

Example 4: Concentric Cylinders -Q R2 +Q R1 L For L >> R2, show:

Solution: