EM & Vector calculus #2 Physical Systems, Tuesday 23 Jan 2007, EJZ
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Transcript of EM & Vector calculus #2 Physical Systems, Tuesday 23 Jan 2007, EJZ
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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/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)
E.dA = q/0=, E = F/q
ldEdr
rV
')'(
4
1)(
VE
F = q E = m a
W = qV
C = q/V
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Conservative fields admit potentials
0 ldE
0 E
b
a
ldEV
depends only on endpoints.Therefore
• 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
V
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Parallel plates
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Electrostatic boundary conditions:
• E is discontinuous across a charge layer: E = /0
• 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