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§2.4 Electric work and energy

§2.4 Electric work and energy. Christopher Crawford PHY 416 2014-10-13. Outline. Electric work and energy Energy of a charge distribution Energy density in terms of E field Field lines and equipotentials Drawing field lines Flux x flow analogy

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§2.4 Electric work and energy

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  1. §2.4Electric work and energy Christopher Crawford PHY 416 2014-10-13

  2. Outline • Electric work and energyEnergy of a charge distributionEnergy density in terms of E field • Field lines and equipotentialsDrawing field linesFlux x flow analogy • Poisson’s equationCurvature of functionGreen’s functionsHelmholtz theorem

  3. Energy of a charge distribution • Reminder of meaning: potential x charge = potential energy • Integrating energy over a continuous distribution • Continuous version

  4. Energy of the electric field • Integration by parts • Derivative chain • Philosophical questions: • is the energy stored in the field, or in the force between the charges? • is the electric field real, or just a calculational device? potential field? • if a tree falls in the forest ...

  5. Superposition • Force, electric field, electric potential all superimpose • Energy is quadratic in fields, not linear • the cross term is the `interaction energy’ between two distributions • the work required to bring two systems of charge together • W1 and W2 are infinite for point charges – self-energy • E1E2 is negative for a dipole (+q, -q)

  6. Flux × Flow: energy/power density

  7. Electric flux and flow FLUX • Field lines (flux tubes)counts charges inside surfaceD = ε0E = flux density ~ charge FLOW • Equipotential (flow) surfacescounts potential diffs. ΔV from a to bE = flow density ~ energy/charge Closed surfaces because E is conservative FLUX x FLOW = ENERGY • Energy density (boxes)counts energy in any volumeD  E ~ charge x energy/charge FLUX x FLOW = ? B.C.’s:Flux lines bounded by charge Flow sheets continuous (equipotentials)

  8. Plotting field lines and equipotentials

  9. Green’s function G(r,r’) • The potential of a point-charge • A simple solution to the Poisson’s equation • Zero curvature except infinite at one spot

  10. Green’s functions as propagators • Action at a distance: G(r’,r) `carries’ potentialfrom source at r' to field point (force) at r • In quantum field theory, potential is quantizedG(r’,r) represents the photon (particle) that carries the force • How to measure `shape’ of the proton?

  11. Putting it all together… • Solution of Maxwell’s equations

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