Physics 2102 Jonathan Dowling Flux Capacitor Schematic Physics 2102 Lecture 05 FRI 23 JAN ersion 1 22 07 Gauss Law I QuickTime and a decompressor are needed to see this Carl Friedrich Gaus 1777 1855 What Are We Going to Learn A Road Map Electric charge Electric force on other electric charges Electric field and electric potential Moving electric charges current Electronic circuit components batteries resistors capacitors Electric currents Magnetic field Magnetic force on moving charges Time varying magnetic field Electric Field More circuit components inductors Electromagnetic waves light waves Geometrical Optics light rays Physical optics light waves What The Flux STRONG E Field Angle Matters Too Weak E Field dA Number of E Lines Through Differential Area dA is a Measure of Strength Electric Flux Planar Surface Given planar surface area A uniform field E E makes angle q with NORMAL to plane Electric Flux E A E A cos Units Nm2 C Visualize Flow of Wind Through Window E normal AREA A An Electric Flux General Surface For any general surface break up into infinitesimal planar patches Electric Flux E dA Surface integral dA is a vector normal to each patch and has a magnitude dA dA CLOSED surfaces define the vector dA as pointing OUTWARDS Inward E gives negative flux Outward E gives positive flux E dA Area dA E dA Electric Flux Example Closed cylinder of length L radius R Uniform E parallel to cylinder axis What is the total electric flux through surface of cylinder a 2 RL E b 2 R2 E R2 E R2 E 0 c Zero What goes in MUST come out Hint Surface area of sides of cylinder 2 RL Surface area of top and bottom caps each R2 dA E L dA R Electric Flux Example Note that E is NORMAL to both bottom and top cap E is PARALLEL to curved surface everywhere So R2E 0 R2E 0 Physical interpretation total inflow total outflow dA 1 2 3 dA dA Electric Flux Example Spherical surface of radius R 1m E is RADIALLY INWARDS and has EQUAL magnitude of 10 N C everywhere on surface What is the flux through the spherical surface a 4 3 R2 E 13 33 Nm2 C b 2 R2 E 20 Nm2 C c 4 R2 E 40 Nm2 C hat could produce such a field What is the flux if the sphere is not centered on the charge Electric Flux Example r q E 2 r r r Inward r dA dA r q r r E dA EdAcos 180 EdA Outward Since r is Constant on the Sphere Remove E Outside the Integral r r E dA E kq dA 2 4 r 2 Surface Area Sphere r q 4 q 0 4 0 Gauss Law Special Case QuickTime and a decompressor are needed to see this picture
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