EM

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EM Vector calculus 4Physical Systems, Tuesday
13 Feb. 2007, EJZ

• Vector Calculus 1.4 Curvilinear Coordinates
• Quick review of quiz and homework
• Review Cartesian coordinates, unit vectors, and
  dl
• Spherical and cylindrical
• Coordinates, unit vectors, dl, and vector
  derivatives
• Ch.3b Finding potentials using separation of
  variables
• Quick review of quiz and homework
• Example 3.3
• Worksheets for Problems 3.12 and 3.23

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Vector calculus HW Quiz review
Online solutions at http//192.211.16.13/curricula
r/physys/0607/solns/ HW VCsoln31.pdf,
EMsoln3a.pdf, EMsoln3b.pdf Quiz VCMidSoln.pdf,
EMmodMidSoln.pdf
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Cartesian Coordinates
The infinitesimal displacement vector from
(x,y,z) to (xdx, ydy, zdz) is dl
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Cylindrical Coordinates
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Spherical Coordinates
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Cylindrical Coordinates
Derive these (Problem 1.41)
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Spherical Coordinates
Derive these (Problem 1.37)
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Vector calculus HW due next week
Ch.1.4 Problems 1.37, 1.38, 1.41, 1.42
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EM Ch.3b Separation of variables

• Quick review of quiz and homework
• When to use separation of variables?
• In charge-free regions
• With well-specified boundary conditions
• Without sufficient symmetry to use Gauss law
• How to use separation of variables?
• Guess form of solutions based on BC
• Separate variables, insert guessed solutions
  with constants
• Apply BC and solve for constants

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Poisson and Laplace equations
Gauss
Potential combine to get Poissons eqn
Laplace equation holds in charge-free regions
Last week we found the general solutions to
Laplaces eqn. in spherical and cylindrical
coordinates for the case where V depends only on
r (Prob.3.3, p.116) ?
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Solving Laplace w/ Separation of Variables
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Worksheets for Problems 3.12 (136), 3.23 (145)
Homework due next week work through Ex.3.3, do
3.12 and 3.23. Extra credit 13, 24.