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Transcript

Gauss’s Law AP Physics C How to use Gauss’s Law Count the lines leaving a surface as + Count the lines entering a surface as – Figures 23-10 and 23-11 on p.696 Gauss’s Law Relates the electric field on a closed surface to the net charge within the system For static charges, Gauss’s Law and Coulomb’s Law are EQUIVALENT Gauss’s Law: The net number of lines leaving any surface enclosing the charges is proportional to the net charge enclosed by the surface Electric Flux Φ The mathematical quantity that corresponds to the number of field lines crossing a surface For a surface perpendicular to the Electric Field, the flux is defined as the product of the magnitude of the field E and the area A: Φ = EA (units are Nm2/C) The box may enclose a charge, by placing a test charge and observing F, we know E. It is only necessary to do this at the surface of the shape. Pictures of outward (+) flux and inward (-) flux Electric Flux Φ continued When the area is NOT perpendicular to E, then the following equation is used: Φ = EAcosθ = EnA Where En is the component of E that is perpendicular or normal to the surface Flux Flux, in this case Electric Flux, is the amount of (electric) field passing through a specified area. Think of water flowing in a pipe (flux comes from the Latin for “flow”) Situations where the total flux equals zero Ф = 0 through triangular prism below. E = 500 N/C 50 cm 30 cm 40 cm 40 cm The E-field decreases at 1/r2 while the area increases at r2 and that increase and decrease cancel each other out and that is why the size of the surface enclosing Q does not matter. Electric Flux Φ continued What if E varies over a surface? (see Fig 23-14 on p.697) If we take very small areas A that can be considered a plane, we can then sum the fluxes for each area using Calculus Flux Symbol ФE Unit Nm2/C Equation: E E A EA cos E E dA Quantitative Statement of Gauss’s Law P698 The net flux through any surface equals 4πk times the net charge inside the surface Gauss’ Law E E dA Qenclosed 0 4 kQenclosed What we can conclude about Ф 1. 2. 3. Ф is proportional to q Whether Ф is inward or outward depends on the q inside the surface A q outside the surface offers zero Ф because Фin = Фout Point Charge Line of Charge Sheet of Charge Uniformly charge insulator at a varying r