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
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)
1.2.1 Ordinary derivatives
1.22 Gradient
1.23 The operator
1.2.4 Divergence
1.2.5 Curl
1.2.6 Product rules
1.2.7 Second derivatives
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)
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
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
Parallel plates
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
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.
Electrostatic potential energy