Agenda Today –Chapter 24 (Finish Fri & Start 25) HMWK Due Fri Return Quiz Friday Reading –Finish ch. 24 by Friday –Skim 25 (at least last page) Friday –Read 25 by Monday

Field vs. Potential Turns Scalar into Vector

Field vs. Potential Gradient: Think Slope of PE plot 3D Fun Potential surrounding + & - charge pair Slope at any given point gives Electric Field

Simple Example Gravity of course

Force from PE Field is same (w.o. the “m”)

Spherical Case Normally quite complicated Wait till calc 3 Radial component only:

Fields in a material? Electric Field changes in a material Example: Metal field = 0 Insulators change as well Interaction of neutral object with a field? Polarization Polarization takes energy (lining up atoms) Some of the energy in the field goes to polarizing material Reduces the effective strength of a field

Mathematically Electric Field of a point charge Equivalent Equations Epsilon (  ) is permittivity How easily field permeates a material  is a material dependent constant  in vacuum is one  in air is one  in materials (insulators) is > 1

Dielectrics Materials used specifically for their permittivities (  or  0 ) Talked about when dielectric properties are important

Dielectric Breakdown When electric field too large Strips electrons from material components Arcing – shorting – lightning Damaging to components (& people!)

How many volts in static electricity? Dielectric Breakdown in air ~ 3x10 6 V/m Units for field V/m or N/C (same thing) Most shocks between mm & cm Assume field constant –Big || plates = finger & cat for example Field = Breakdown field V ranges from 1 to 10 kV Deadly?

Dielectric Usage Stores Field energy in form of polarization Can be used as electrical energy storage Capacitors

Simplest Form: || Plate Apply Voltage Across Parallel Plates V = Ed E (plate) =    E (Between) =     = Q/A Infinite just approximation E = Q/(A  0 ) V = Ed V = Qd / (A  0 )

Simplest Form: || Plate Apply Voltage Across Parallel Plates V = Qd / (A  0 ) Capacitance = Ability to store Charge from V Q = V C [C is capacitance] V = Q / C || plate: C = A  0 /d Examine parameters Geometric & material only, no field dep.

Energy Storage: Capacitor Consider how much energy it takes to move charges from one plate to another “Assemble” Charges Work done in moving charges stored as Potential Energy

Energy Storage: Capacitor Can Apply Top Equation to Bottom Mix & Match, Q,V,C As usual, ½  Integration

Other Geometries Spherical, other all have different formulas for capacitance Universal: –C depends only on dielectric & geometry –Q = VC –PE = Q 2 /2C

Agenda Today –Chapter 24 (Finish Fri & Start 25) HMWK Due Fri Return Quiz Friday Reading –Finish ch. 24 by Friday –Skim 25 (at least last page) Friday –Read 25 by Monday