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EM & Vector calculus #2 Physical Systems, Tuesday 23 Jan 2007, EJZ

EM & Vector calculus #2 Physical Systems, Tuesday 23 Jan 2007, EJZ. Vector Calculus 1.2: Differential Calculus Ordinary derivatives Div, Grad, and Curl Product rules, Second derivatives Ch.2 Electrostatic potential and energy Quick homework review

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EM & Vector calculus #2 Physical Systems, Tuesday 23 Jan 2007, EJZ

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  1. EM & Vector calculus #2Physical Systems, Tuesday 23 Jan 2007, EJZ • Vector Calculus 1.2: Differential Calculus • Ordinary derivatives • Div, Grad, and Curl • Product rules, Second derivatives • Ch.2 Electrostatic potential and energy • Quick homework review • Review electrostatics, Gauss’ Law: charges  E field • Conservative fields and path independence  potential V • Boundary conditions (Ex. 2.5 p.74, Prob. 2.30 p.90) • Electrostatic energy (Prob. 2.40 p.106), capacitors (Ex. 2.10 p.104)

  2. 1.2.1 Ordinary derivatives

  3. 1.22 Gradient

  4. 1.23 The  operator

  5. 1.2.4 Divergence

  6. 1.2.5 Curl

  7. 1.2.6 Product rules

  8. 1.2.7 Second derivatives

  9. Electrostatic potential and energyEM # 2, Physical Systems, Tuesday 23 Jan 2007, EJZ • Quick homework review • Review electrostatics, Gauss’ Law: charges  E field • Conservative fields and path independence  potential V • Boundary conditions (Ex. 2.5 p.74, Prob. 2.30 p.90) • Electrostatic energy (Prob. 2.40 p.106), capacitors (Ex. 2.10 p.104)

  10. Ch.2: Electrostatics (d/dt=0): charges  fields  forces, energy • Charges make E fields and forces • charges make scalar potential differences dV • E can be found from V • Electric forces move charges • Electric fields store energy (capacitance) F = q E = m a W = qV C = q/V

  11. Therefore depends only on endpoints. Conservative fields admit potentials • Easy to find E from V • is independent of choice of reference point V=0 • V is uniquely determined by boundary conditions • Every central force (curl F = 0) is conservative (prob 2.25) • Ex.2.5 p.74: parallel plates

  12. Parallel plates

  13. Electrostatic boundary conditions: • E is discontinuous across a charge layer: DE = s/e0 • E||and V are continuous • Prob 2.30 (a) p.90: check BC for parallel plates

  14. Electrostatic potential: units, energy Prob. 2.40 p.106: Energy between parallel plates Ex. 2.10 p.104:Find the capacitance between two metal plates of surface area A held a distance d apart.

  15. Electrostatic potential energy

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