1
1
Gauss’ Law – I
Carl Friedrich Gauss
17771855
This lecture: HRW 23.123.5
For next time: HRW 23.623.9
2
Last Week
•
Electric Field
–
A vector field that pervades space
–
The electric force on a particle is the field times its charge
•
Electric field lines help visualize electric fields
–
The density of lines is proportional to the magnitude of the field
–
The electric field is tangent to the electric field line
•
How to calculate the electric field from:
–
Collections of point charges
–
Continuous charge distributions
Today
•
Electric Flux
•
Gauss’ Law
–
Spherical symmetry
–
Cylindrical symmetry
–
Planar symmetry
3
E
d
a
a
E
Area =
a
Electric flux
–
da
is a
vector
normal to each
patch in the
outward direction
,
and has a magnitude
a
.
–
Inward E
gives
negative
Φ
–
Outward E
gives
positive
The
total flux
is the sum over all the
surface elements:
Any surface can be broken up into infinitesimal planar patches.
The
Electric Flux
through a patch is given by
r
r
dd
Φ
= E •
a
==
•
∫∫
r
r
ΦΦ
Ea
surface
integral
4
θ
E
Area = A
normal
Electric Flux through a Planar
Surface
For the special case of a planar surface
of area, A, and a uniform field, E,
that makes an angle
with respect to
normal:
ˆˆ
ˆ
.
•=
•
•
∫
∫
r
r
r
Φ
=EnA En A
=E nA =
EAcos
θ
Qualitatively,
flux is the number
of field lines crossing an area A.
Units of flux:
N m
2
/C
Why the dot product? It’s like the “flow
of water” through a surface. Eg., the flux
through all these surfaces is the same.
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 Spring '07
 HUANG,TAIYIN
 Charge, Electric Fields, Electrostatics, Gauss' Law, Magnetism, Force, Magnetic Field, Electric charge, Carl Friedrich Gauss, Interactive Lecture Question

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