1 / 16

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

marshall-jaidyn
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related