Slide 1Slide 2Electric FluxSlide 4Electric Flux Through Angled SurfacesSlide 6Slide 7Slide 8Gauss’ LawElectric Field of a Charged Thin Spherical ShellSlide 11Electric Field of a Nonconducting Plane Sheet of Charge, cont.Parallel Plate CapacitorConductors in Electrostatic EquilibriumProperty 3Slide 16Lightning Rod EffectSlide 18Van de Graaff GeneratorSlide 20Work and Potential EnergySlide 22Slide 23Slide 24Slide 25Physics 213General PhysicsLecture 32 Last Meeting: Electric Field, ConductorsToday: Gauss’s Law, Electric Energy and PotentialElectric FluxField lines penetrating an area A perpendicular to the fieldThe product of EA is the flux, ΦIn general:ΦE = E A cos θ4Demo (Flux) Pivoting rectangleElectric Flux Through Angled Surfaces67Demo Styrofoam ball with toothpicks8qGauss’ LawGauss’ LawGauss’ Law states that the electric flux outward through any closed surface is equal to the net charge Q inside the surface divided by εoεo is the permittivity of free space and equals 8.85 x 10-12 C2/Nm2The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical objectinsideEoQ Electric Field of a Charged Thin Spherical ShellThe calculation of the field outside the shell is identical to that of a point chargeThe electric field inside the shell is zero2eo2rQkr4QE 11Electric Field of a Nonconducting Plane Sheet of Charge02Electric Field of a Nonconducting Plane Sheet of Charge, cont. The field must be perpendicular to the sheet The field is directed either toward or away from the sheetParallel Plate CapacitorThe device consists of plates of positive and negative chargeThe total electric field between the plates is given byThe field outside the plates is zerooEConductors in Electrostatic EquilibriumWhen no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibriumAn isolated conductor has the following properties:1. The electric field is zero everywhere inside the conducting material.2. Any excess charge on an isolated conductor resides entirely on its surface.3. The electric field just outside a charged conductor is perpendicular to the conductor’s surface.4. The charge accumulates at locations where the radius of curvature of the surface is smallest (that is, at sharp points).Property 3The electric field just outside a charged conductor is perpendicular to the conductor’s surfaceConsider what would happen it this was not trueThe component along the surface would cause the charge to moveIt would not be in equilibrium16In a conductor electrons are free to move. If a conductor is placed into E, a force F = -eE acts on each free electron. Soon electrons will pile up on the surface on one side of the conductor, while the surface on the other side will be depleted of electrons and have a net positive charge. These separated negative and positive charges on opposing sides of the conductor produce their own electric field, which opposes the external field inside the conductor and modifies the field outside. Electrons inside the conductor experience no force.Lightning Rod EffectAny excess charge moves to its surfaceThe charges move apart until an equilibrium is achievedThe amount of charge per unit area is greater at the flat endThe forces from the charges at the sharp end produce a larger resultant force away from the surfaceWhy a lightning rod works18Demo Van de Graaff GeneratorVan de GraaffGeneratorCharge is transferred to the dome by means of a rotating belt20Work and Potential EnergyThere is a uniform field between the two platesAs the charge moves from A to B, work is done on itW = Fd=q Ex (xf – xi)ΔPE = - W = - q Ex xOnly for a uniform field22232425[V] =
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