(prev) | (top) | (next) |

- The
**capacitance**of a**capacitor**for storing charge is the ratio of the charge stored to the potential difference "across" the capacitor:C ≡ Q / ΔV.

Capacitance is measured in

**Farads**(1 F ≡ 1 C / V). Note that ε also has units of F / m.Capacitance depends only on the geometry of the capacitor and the permittivity. To compute the capacitance, use Gauss' law to compute E and integrate to get ΔV.

- Two electrical components are said to be in
**series**if they are connected directly together at one end of each, and nothing else is connected there:Any charge that enters one side of a series configuration

Two capacitors in series have the same charge, so if we replace them with an equivalent capacitor, we must have*must*leave the other side.Q

or_{eq}= Q_{1}= Q_{2}ΔV

_{eq}= ΔV_{1}+ ΔV_{2}1 / C

_{eq}= 1 / C_{1}+ 1 / C_{2} - Two electrical components are said to be in
**parallel**if they are connected directly together at both ends, and nothing else is connected between them:Since conductors are equipotentials, components in a parallel configuration

Two capacitors in parallel have the same ΔV ("voltage drop"), so if we replace them with an equivalent capacitor, we must have*must*be at the same potential where they are connected.ΔV

or_{eq}= ΔV_{1}= ΔV_{2}Q

_{eq}= Q_{1}+ Q_{2}C

_{eq}= C_{1}+ C_{2} - The work required to charge a capacitor is
∫ ΔV dq

If we think of this energy as being stored in the electric field within the capacitor, we can compute the= Q

^{2}/ (2 C)= C ΔV

^{2}/ 2.**energy density**of the electric field to beu

(This can be shown using a parallel plate capacitor:_{E}= ε E^{2}/ 2.C ΔV

but it is true in general.)^{2}/ 2 / (area * distance) = ε ΔV^{2}/ (2 distance^{2})= ε (E * distance)

^{2}/ (2 distance^{2}) - This applet will allow you to practice analysis of some simple capacitor networks (for the moment, ignore the questions involving resistors).
- Define the
**dipole moment**of two oppositely charged particles (± q), separated by a distance r, as**p**≡ q**r**,**r**points from -q to +q. Then the torque experienced by the dipole in an electric field is**τ**=**p ⊗ E**U = -

**p ⋅ E**.

(prev) | (top) | (next) |

©2011, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.