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§2.2 Div. and Curl of E

§2.2 Div. and Curl of E. Christopher Crawford PHY 416 2014-10-06. Outline. 5 Formulations of electrostatics Derivative chain Flux and Flow of electric field Electric flux Gauss ’ law Three applications Electric flow Irrotational / conservative electric field Electric potential

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§2.2 Div. and Curl of E

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  1. §2.2Div. and Curl of E Christopher Crawford PHY 416 2014-10-06

  2. Outline • 5 Formulations of electrostaticsDerivative chainFlux and Flow of electric field • Electric fluxGauss’ lawThree applications • Electric flowIrrotational / conservative electric fieldElectric potential • Recovery of Coulomb’s lawHelmholtz theorem

  3. 5 Formulations of Electrostatics • All electrostatics comes out of Coulomb’s law & superposition • Note: every singletheorem ofvector calculus! • Flux and Flow:Schizophrenicpersonalities of E • Integral vs. differential • Purpose of eachformulation V  E Q • Derivative chains:

  4. Electric flux and flow FLUX • Field linescounts charges inside surfaceE = flux density • The flux counts the amountof charge inside the surface FLOW • Equipotential surfacescounts flow along any pathE = flow density • The surfaces are closed: E is a conservative field Flow = change in potential ΔV B.C.’s:Flux lines bounded by charge Flow sheets continuous (equipotentials)

  5. Gauss’ law • Integral form • Differential form – divergence theorem • Direct calculation of divergence

  6. Three applications of Gauss’ law • Plane – surface charge – boundary conditions • Cylinder – line charge • Sphere – point charge

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