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Electrostatic Formulations & Applications: Exploring Flux and Flow in Electric Fields

Understand the five formulations of electrostatics, including flux, flow, electric potential, and recovery of Coulomb's law, through Gauss' law and the Helmholtz theorem. Explore electric field derivatives and their applications in conservative fields.

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Electrostatic Formulations & Applications: Exploring Flux and Flow in Electric Fields

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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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