PhysCh23章节幻灯片.pptVIP

Ch 23. Gauss’ Law (高斯定律) To use Gauss’s law to calculate electric fields We first introduce the concept of electric flux (电通量) phi Vectors - others Surface Vector Vectors - others Two conventions: Vectors - others Two conventions: Consider a closed surface Positive charge within the box produces outward electric flux through the surface of the box, and negative charge produces inward flux. Zero net charge inside a box Below shows three cases in which there is zero net charge inside a box and no net electric flux through the surface of the box. Example : S1 : positive flux S2 : negative flux S3 : zero flux S4 : zero flux Example : no charge enclosed Gauss’ Law Gauss’ law relates the net flux Φ of an electric field through a closed surface (a Gaussian surface) to the net charge qenc that is enclosed by that surface What affects the flux through a box? Doubling the charge within the box doubles the flux, but doubling the size of the box does not change the flux. The electric flux through a Gaussian surface is proportional to the net number of electric field lines passing through that surface. E-field of a charged conducting sphere Sketch the E-field against the distance r Planar symmetry A thin, flat infinite sheet with a uniform positive surface charge density σ Planar symmetry We will use this approximation +σ -σ Cylindrical symmetry if a x Using Coulomb’s law : = Example – uniform + charge in insulating sphere Positive charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R. Find the magnitude of the E-field at a point P a distance r from the center of the sphere For E inside the sphere, r R Volume charge density ρ : Total charge enclosed by the Gaussian surface : By Gauss’ Law : → Example – uniform charge in insulating sphere For E inside the sphere, r R For E outside the sphere, r R Sketch the graph of E vs r E r R Charged isolated conductor Enclosed no charge Enclosed no charge Electrostatic shielding A conducting b