Chapter 22Gauss’s LawDr. Ray KwokSJSUGauss's Law - Dr. Ray KwokGoals for Chapter 22• To study electric flux• To calculate electric flux with Gauss’s Law• To consider the electric field of various symmetric charge distributionsGauss's Law - Dr. Ray KwokGaussCarl Friedrich GaussGerman mathematician & scientist1777 - 1855 In cgs, gauss is the unit for magnetic field.Many contributions in math and geophysics.Most known for his electrostatic work….Known as the Gauss’s Law.Gauss's Law - Dr. Ray KwokElectric Flux Field lines penetrating an area A perpendicular to the field The product of EA is the flux, Φ In general: ΦE= E A cos θ∫⋅≡Φ adEErrGauss's Law - Dr. Ray KwokA measurement of flux will be sensitiveto measurement orientationGauss's Law - Dr. Ray KwokFlux in a uniform fieldGauss's Law - Dr. Ray KwokGauss’ Law Gauss’ Law states that the electric flux through any closed surface is equal to the net charge Q inside the surface divided by εo εois the permittivity of free space and equals 8.85 x 10-12C2/Nm2 The area in Φ is an imaginary surface, a Gaussian surface, it does not have to coincide with the surface of a physical objectinsideEoQεΦ =∫ε=⋅oinsideQadErrGauss's Law - Dr. Ray KwokFlux as the flow out of an imagined boxinsideEoQεΦ =Gauss's Law - Dr. Ray KwokFlux considerationinsideEoQεΦ =Gauss's Law - Dr. Ray KwokTotal flux does not depends on the shape chosenGauss's Law - Dr. Ray KwokIntegrating over all surfaces∫ε=⋅oinsideQadErrdon’t forget the dot productGauss's Law - Dr. Ray KwokGaussian Surface Have the same symmetry as the charge distribution, such that… E field is uniform on the surface E field is perpendicular to the surfaceEAadEE=⋅≡Φ∫rroinsideQEAε=Gauss's Law - Dr. Ray Kwoke.g. Point ChargeGaussian surface is a sphere( )2oo2oinsiderq41Eqr4EQEAπε=ε=πε=which is the E field for a point chargeGauss's Law - Dr. Ray KwokE Field of a Charged Thin Spherical Shell The calculation of the field outside the shell is identical to that of a point charge The electric field inside the shell is zero2eo2rQkr4QE =επ=Gauss's Law - Dr. Ray KwokE field of a charged conductorsame….Gauss's Law - Dr. Ray KwokE field of a line or plane of chargeinfinite line chargeinfinite plane of chargeGauss's Law - Dr. Ray KwokE field of a uniformly charged sphereGauss's Law - Dr. Ray KwokEffect of changing the sign of the chargeGauss's Law - Dr. Ray KwokCharges on conductorsGauss's Law - Dr. Ray KwokA Faraday CageSci-Fi movie – to prevent alien