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F16 PH 333 2.2.1-2.2.4

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Richard Datwyler

on 2 October 2018

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Transcript of F16 PH 333 2.2.1-2.2.4

Divergence and Curl of Electrostatic Fields
2.2.1-2.2.4
2.2.1 Field lines, Flux, Gauss's Law
2.2.2 The divergence of E
2.2.3 Using Gauss's Law
2.2.4 The Curl of E
2.2.1
Some integrals are hard. Here we start simplifications. ( but these have issues of only working in nice symmetries)
Field lines:
Never cross
start at + end at - (infinity is ok for either too)
Density matters
Flux is:
Gauss's Law
Using the Divergence theorem, how can we express the LHS of Gauss's law?
D
C
B
A
By definition how can we find the Q enclosed inside the same volume?
D
C
B
A
Together:
or in differential form
Back to divergence of E 2.2.2
Recall
Take the divergence of both sides.
with
Gives
Gauss's law
differential form
2.2.3 Using Gauss's Law
Always true. But not always easy (useful)
E is constant on surface
E is perpendicular to surface
E is parallel to surface
Nice symmetries exist
All the above
Which of these conditions must be met to make it easy (useful)
A
B
C
D
E
Symmetries
Spherical Symmetry
Cylindrical Symmetry
Planar Symmetry
Choose Gaussian surface to match the symmetry
L
R
A Gaussian cylinder sits in a constant E field as shown, what is the total E Flux through the Gaussian surface?
D
C
B
A
Practice
Practice
Curl of E
Choose a point charge.
by inspection
more rigorously, take any path by this point charge.
If the path closed, then = zero
ANY E FIELD
Q
2Q
5
4
3
2
1
d
c
b
a
Two large conductors have charges Q and 2Q and top surfaces A. What is the E field in each region 1-5 and surface charge density a-d
"Could you explain the Gaussian pillbox a little better? I am having a hard time picturing it. "
"Can we go through the derivation of the Divergence of E? I want to see and better understand how the separation vector applies in the integral."
"Could we go over how to to draw the electric field lines when there are multiple charges?"
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