EEE 498/598 Overview of Electrical Engineering. Lecture 3: Electrostatics: Electrostatic Potential; Charge Dipole; Visualization of Electric Fields; Potentials; Gauss’s Law and Applications; Conductors and Conduction Current. Lecture 3 Objectives.
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Lecture 3:
Electrostatics: Electrostatic Potential; Charge Dipole; Visualization of Electric Fields; Potentials; Gauss’s Law and Applications; Conductors and Conduction Current
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2
Q2
P(R,q,f)
Q1
O
No longer spherically symmetric!
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line charge
surface charge
volume charge
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Q Distributions
+Q
d
Charge Dipole6
+Q Distributions
Q
Dipole Momentp isin the direction from the negative point charge to the positive point charge
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not good
enough!
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q
d/2
d/2
lines approximately
parallel
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S FarField (Cont’d)
ds
V
Gauss’s Law (Cont’d)By convention, ds
is taken to be outward
from the volume V.
Since volume charge
density is the most
general, we can always write
Qencl in this way.
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known
unknown
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Q FarField (Cont’d)
Electric Flux Density of a Point Charge Using Gauss’s LawConsider a point charge at the origin:
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(1) Assume from symmetry the form of the field
(2) Construct a family of Gaussian surfaces
spherical symmetry
spheres of radius r where
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(3) Evaluate the total charge within the volume enclosed by each Gaussian surface
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(4) For each Gaussian surface, evaluate the integral
surface area
of Gaussian
surface.
magnitude of D
on Gaussian
surface.
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(5) Solve for D on each Gaussian surface
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a (Cont’d)
b
Electric Flux Density of a Spherical Shell of Charge Using Gauss’s LawConsider a spherical shell of uniform charge density:
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(1) Assume from symmetry the form of the field
(2) Construct a family of Gaussian surfaces
spheres of radius r where
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a Gauss’s Law (Cont’d)
b
Electric Flux Density of a Spherical Shell of Charge Using Gauss’s Law (Cont’d)1)
2)
3)
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Gaussian surfaces
for which
Gaussian surfaces
for which
Gaussian surfaces
for which
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(3) Evaluate the total charge within the volume enclosed by each Gaussian surface
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(4) For each Gaussian surface, evaluate the integral
surface area
of Gaussian
surface.
magnitude of D
on Gaussian
surface.
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(5) Solve for D on each Gaussian surface
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Total charge contained
in spherical shell
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0.7 Gauss’s Law (Cont’d)
0.6
0.5
0.4
(C/m)
r
D
0.3
0.2
0.1
0
0
1
2
3
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5
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R
Electric Flux Density of a Spherical Shell of Charge Using Gauss’s Law (Cont’d)48
Consider a infinite line charge carrying charge per
unit length of qel:
z
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(1) Assume from symmetry the form of the field
(2) Construct a family of Gaussian surfaces
cylinders of radius r where
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(3) Evaluate the total charge within the volume enclosed by each Gaussian surface
cylinder is
infinitely long!
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(4) For each Gaussian surface, evaluate the integral
surface area
of Gaussian
surface.
magnitude of D
on Gaussian
surface.
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(5) Solve for D on each Gaussian surface
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V Gauss’s Law (Cont’d)
S
Recall the Divergence Theorem55
Because the above must hold for any
volume V, we must have
Differential form
of Gauss’s Law
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e Gauss’s Law (Cont’d)
Conduction Currente = 1.602 1019C
magnitude of electron charge
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Electron mobility
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E = 0
+
+
+
+
+
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