Electricity and MagnetismMore on Electric Flux and Gauss’ LawElectric FluxA?Electric FluxGauss’ LawGauss’ LawUse the Symmetry!Use the Symmetry!Use the Symmetry!Use the Symmetry!Hollow conducting SphereLast exampleFaraday CageFaraday Cage‘Challenge’ In-Class DemoFeb 20 2002Electricity and Magnetism•More on– Electric Flux– Gauss’ LawFeb 20 2002More on Electric Flux and Gauss’ LawMaxwell Equations(1873)Feb 20 2002Electric FluxElectric Flux ΦE= E ANote absence of ‘ ‘‘ΦE’ is a Scalar: How much?I.e. how much field passes through surface A?Feb 20 2002A?•Direction– Normal to surface•Magnitude–Surface Area• For closed surface– Pointing outwardsFeb 20 2002Electric Flux• What if E not constant on surface A?•Use integral• Often, ‘closed’ surfacesFeb 20 2002Gauss’ Law• Connects Flux through closed surface and charge inside this surface:Note: k = 1/ 4 π ε0Feb 20 2002Gauss’ Law• True for ANY closed surface around Qencl• Suitable choice of surface A can make integral very simpleFeb 20 2002Use the Symmetry!+QPoint ChargedA+QSpherical SurfaceFeb 20 2002Use the Symmetry!++++++++++++++++++++++r0Spherical SurfacesA1A2++++++++++++++++++++++r0Charged SphereFeb 20 2002Use the Symmetry!++++++++++++++++++++++r0Spherical SurfacesA1A2Feb 20 2002Use the Symmetry!Charged Line Cylindrical Surface++++++++ ++++++ ++Feb 20 2002Hollow conducting Sphere++++++++++++++++++++++++++++++++++Feb 20 2002Last example+ +++++++ ++++++Feb 20 2002Faraday Cage++++++++++HV--- --Van der Graaf GeneratorHollow Metal Sphere Figure by MIT OCW.Feb 20 2002Faraday Cage+++++++++Van der Graaf GeneratorHollow Metal Sphere Large E; E~1/r2Figure by MIT OCW.Feb 20 2002‘Challenge’ In-Class
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