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Chapter 23 gauss's law

Chapter 23 gauss's law

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Chapter 23: Gauss’s Law Gauss’s Law • Gauss’s Law is the first of the four Maxwell Equations which summarize all of electromagnetic theory. • Gauss’s Law gives us an alternative to Coulomb’s Law for calculating the electric field due to a given distribution of charges. Gauss’s Law: The General Idea The net number of electric field lines which leave any volume of space is proportional to the net electric charge in that volume. E lines leaving V volume V E lines entering V Flux The flux Φ of the field E through the surface S is defined as r r Φ = ∫ E ⋅ dA S The meaning of flux is just the number of field lines passing through the surface. Best Statement of Gauss’s Law The outward flux of the electric field through any closed surface equals the net enclosed charge divided by ε0. Gauss’s Law: The Equation r r E ⋅ d A = Q / ε 0 enc ∫ S • S is any closed surface. • Qenc is the net charge enclosed within S. • dA is an element of area on the surface of S. • dA is in the direction of the outward normal. ε 0 = 8.85 × 10 −12 SI units Flux Examples Assume two charges, +q and –q. Find fluxes through surfaces. Remember flux is negative if lines are entering closed surface. Φ1 = +q/ε0 Φ2 = –q/ε0 Φ3 = 0 Φ4 = (q –q )/ε0 = 0 Another Flux Example Given uniform field E, find flux through net. Must have closed surface, so let S be (net+circle). Then Qenc = 0 so Gauss’s law says ΦS = 0. But Φ circle = π a E ...
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