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Chapter 22
Electric Flux,
Φ
E
,
and Gauss’s Law
Special Note:
January 17, 2006 was the 300
th
Birthday of Benjamin Franklin–
his letters to the Royal Society around 1750 laid the foundation for understanding
electric charge and protecting buildings from lightning damage.
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View Full Document Electric Field Lines
(Faraday’s Lines of Force)
(helpful visualizer of
)
E
Electric Field lines are drawn such that:
1.
at any point is tangent to the line
2. Lines begin on + charge (or ∞), end on  (or ∞)
1. E is large where the lines are closely spaced
E
Reminder from
last lecture….
Let’s make #3 more quantitative…….
.
Point #3 improved (better)
(E = # of lines, N, per area, A
┴
,
perpendicular to E)
⊥
=
A
N
E
BUT……what if E is varying in magnitude and/or direction over A??
Solution: we need to
shrink A
┴
down to an
infinitesimal, dA
┴
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View Full Document Point #3 improved (best)
⊥
=
=
dA
dN
E
E
Shrink A
┴
to an infinitesimal dA
┴
and consider the infinitesimal number of
lines dN poking through it.
The ratio is the E field
at that point:
This is a dumb way to define our most fundamental concept of E!!
Turn it around to define N in a fundamental fashion…….
⊥
=
EdA
dN
How do we get dA
┴
at a selected point on some arbitrary surface???
The outward surface normal
The orientation of a little “swatch” of surface is specified by it’s vector
normal (perpendicular) to the surface of magnitude dA
Equivalently, we can use the unit
vector normal to the surface,
n
ˆ
dA
dA
┴
Note that dA
┴
= dAcosφ and is the component of dA perpendicular to E
We can also define E
┴
= Ecosφ to be the component of E along dA or
n
ˆ
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View Full DocumentDefining the FLUX, Φ
E
, of the Electric Field
≡
≡
⋅
=
=
=
=
⊥
⊥
N
A
d
E
dA
E
EdA
EdA
dN
A
through
E
of
flux
A
area
total
over the
integrate
surface,
finite
any
for
cos
ϕ
DEMO the FLUX!
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This note was uploaded on 04/01/2008 for the course PHYSICS 260 taught by Professor Evrard during the Fall '07 term at University of Michigan.
 Fall '07
 Evrard
 Charge

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