EM

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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)

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1.2.1 Ordinary derivatives
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1.22 Gradient
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1.23 The ? operator
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1.2.4 Divergence
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1.2.5 Curl
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1.2.6 Product rules
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1.2.7 Second derivatives
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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)

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Ch.2 Electrostatics (d/dt0) 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
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Conservative fields admit potentials

• Easy to find E from V
• is independent of choice of
  reference point V0
• 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

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Parallel plates
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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

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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.
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Electrostatic potential energy