P WARNING: Exam 1 Week from Thursday

P Class 09: Outline Hour 1: Conductors & Insulators Expt. 4: Electrostatic Force Hour 2: Capacitors

P Last Time: Gauss’s Law

P Gauss’s Law In practice, use symmetry: Spherical (r) Cylindrical (r, ) Planar (Pillbox, A)

P Conductors

P Conductors and Insulators A conductor contains charges that are free to move (electrons are weakly bound to atoms) Example: metals An insulator contains charges that are NOT free to move (electrons are strongly bound to atoms) Examples: plastic, paper, wood

P Conductors Conductors have free charges  E must be zero inside the conductor  Conductors are equipotential objects

P Conductors in Equilibrium Conductors are equipotential objects: 1) E = 0 inside 2) Net charge inside is 0 3) E perpendicular to surface 4) Excess charge on surface

P Conductors as Shields

P Hollow Conductors Charge placed INSIDE induces balancing charge INSIDE

P Hollow Conductors Charge placed OUTSIDE induces charge separation on OUTSIDE

P PRS Setup What happens if we put Q in the center?

P PRS Questions: Point Charge Inside Conductor

P Demonstration: Conductive Shielding

P Field Enhancement E field is enhanced at sharp points!

P Demonstration: Field Enhancement

P Experiment 4: Electrostatic Force

P Demonstration: Capacitor

P09 - Capacitors and Capacitance

P09 - Capacitors: Store Electric Energy Capacitor: two isolated conductors with equal and opposite charges Q and potential difference  V between them. Units: Coulombs/Volt or Farads

P Parallel Plate Capacitor

P Calculating E (Gauss’s Law) Alternatively could have superimposed two sheets

P Parallel Plate Capacitor C depends only on geometric factors A and d

P Spherical Capacitor Two concentric spherical shells of radii a and b Gauss’s Law  E ≠ 0 only for a < r < b, where it looks like a point charge: What is E?

P Spherical Capacitor For an isolated spherical conductor of radius a: Is this positive or negative? Why?

P Capacitance of Earth For an isolated spherical conductor of radius a: A Farad is REALLY BIG! We usually use pF ( ) or nF (10 -9 )

P PRS Question: Changing C Dimensions

P Demonstration: Changing C Dimensions

P Energy Stored in Capacitor

P Energy To Charge Capacitor 1.Capacitor starts uncharged. 2.Carry +dq from bottom to top. Now top has charge q = +dq, bottom -dq 3.Repeat 4.Finish when top has charge q = +Q, bottom -Q

P Work Done Charging Capacitor At some point top plate has +q, bottom has –q Potential difference is  V = q / C Work done lifting another dq is dW = dq  V

P So work done to move dq is: Total energy to charge to q = Q: Work Done Charging Capacitor

P Energy Stored in Capacitor Since Where is the energy stored???

P Energy Stored in Capacitor Parallel-plate capacitor: Energy stored in the E field!

P PRS Question: Changing C Dimensions Energy Stored

P Batteries & Elementary Circuits

P Ideal Battery Fixes potential difference between its terminals Sources as much charge as necessary to do so Think: Makes a mountain

P Batteries in Series V1V1 V2V2 Net voltage change is  V =  V 1 +  V 2 Think: Two Mountains Stacked

P Batteries in Parallel Net voltage still  V Don’t do this!

P Capacitors in Parallel

P Capacitors in Parallel Same potential!

P Equivalent Capacitance ?

P Capacitors in Series Different Voltages Now What about Q?

P Capacitors in Series

P Equivalent Capacitance (voltage adds in series)

P Dielectrics

P Demonstration: Dielectric in Capacitor

P Dielectrics A dielectric is a non-conductor or insulator Examples: rubber, glass, waxed paper When placed in a charged capacitor, the dielectric reduces the potential difference between the two plates HOW???

P Molecular View of Dielectrics Polar Dielectrics : Dielectrics with permanent electric dipole moments Example: Water

P Molecular View of Dielectrics Non-Polar Dielectrics Dielectrics with induced electric dipole moments Example: CH 4

P Dielectric in Capacitor Potential difference decreases because dielectric polarization decreases Electric Field!

P Gauss’s Law for Dielectrics Upon inserting dielectric, a charge density  ’ is induced at its surface What is  ’?

P Dielectric Constant  Dielectric weakens original field by a factor  Gauss’s Law with dielectrics: Dielectric constants Vacuum1.0 Paper 3.7 Pyrex Glass 5.6 Water 80

P Dielectric in a Capacitor Q 0 = constant after battery is disconnected Upon inserting a dielectric:

P Dielectric in a Capacitor V 0 = constant when battery remains connected Upon inserting a dielectric:

P PRS Questions: Dielectric in a Capacitor

P Group: Partially Filled Capacitor What is the capacitance of this capacitor?