1. 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

2. 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 = F F is a LOT of stored charge !!!

3. 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

4. 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

5. 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

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

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

8. 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.

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

10. Solution: