Gauss’s Law
Electric Flux in a uniform electric field
electric flux
E
Φ
(E
⊥
A)
E is not perpendicular to A
Vector formula for electric flux:
Note:
•
E is proportional to N/
A
⊥
, which means that N is proportional to E
A
⊥
= electric flux (N
being the number of field lines passing through
A
⊥
)
Electric Flux in a nonuniform electric field
Split the surface into
n
small surfaces (
1
2
,
,...,
n
A
A
A
V V
V
)
such that:
1) the surface can be considered flat
2) the electric field varies so little that it can be considered uniform
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View Full DocumentNote:
•
denotes integration over a closed surface
•
A
v
is defined as a vector with magnitude A, and direction
⊥
to and pointing out from the
surface
Electric Flux and Field Lines
•
Flux entering an enclosed volume is negative (
cos
0
E
dA
θ
<
, net flux into)
•
Flux leaving an enclosed volume is positive (
cos
0
E
dA
, net flux out)
•
Flux entering and leaving an enclosed volume is zero (no net flux)
(remember
cos
E dA
E
dA
=
v
v
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 Spring '10
 malkan
 Electrostatics, Magnetic Field, Electric charge, gaussian surface

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