Presentation on theme: "Unit 1 Day 10 Electric Flux & Gauss’s Law"— Presentation transcript:
1 Unit 1 Day 10 Electric Flux & Gauss’s Law Definition of Electric FluxElectric Flux thru a Closed SurfaceGauss’s LawDerivation of Gauss’s Law from Coulomb’s Law
2 Karl Friedrich Gauss 1777-1855 Developed a generalized and more elegant relationshipbetween charge and theelectric field (Coulomb’s Law)
3 Electric FluxThe electric flux refers to the electric field lines that penetrate a given surfaceFor a given uniform electric field E passing thru an area A, the electric flux is defined as:
4 Electric Fluxθ is the angle between the E-Field and the line drawn normal to the surfaceThe electric flux thru an area is proportional to the number of E-Field Lines passing thru the area
5 Electric Flux Thru a Closed Surface In general, an electric fieldis not uniform and the areais not flat !Any area can be divided upinto n number of small elementsof surface area ΔA, sufficiently small to beconsidered flat and the E-field is ratherinvariant over this small area. Then:
6 Electric Flux Thru a Closed Surface In the limit as the sum becomes an integralThen a surface of any shape that completely encloses a volume of space is given by
7 Electric Flux Thru a Closed Surface A (+) flux leaving the volumeA (-) flux entering the volumeIf every field line that enters a volume exits the volume, then: ; thereis no net flux into or out of the closed surfaceThe net flux will be non-zero only if the surface encloses a net chargeThe value of depends on the charge enclosed by the surface. This is Gauss’s Law !