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ElectricityElectric Flux and Gauss’s Law
1
Electric Flux
Gauss’s Law
Electric Field of Spheres
Other Gaussian Surfaces
Point Charges and Spheres
ElectricityElectric Flux and Gauss’s Law
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Flux is defined as the amount of an electric field passing perpendicularly through a surface.
For an electric field passing perpendicular to a plane, it is…
A
EA
E
ElectricityElectric Flux and Gauss’s Law
3
What if the electric field is not perpendicular?
A
A
cosE EAA
θ
AcosEA
E
E
ElectricityElectric Flux and Gauss’s Law
4
What if the surface is a closed surface?
q
E cos4 2rE
kqrr
kq 44 22
ElectricityElectric Flux and Gauss’s Law
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In general, Gauss’ Law states that for any imaginary closed surface
0
insideinside4
QkQ
Gauss’ law is always true but not always useful.
Qinside is the charge inside the imaginary surface.
is the total flux through this surface.
We use Gauss’ law to calculate E.
Gauss’ law is easy to use if the electric field vector is perpendicular to the chosen surface.)
ElectricityElectric Flux and Gauss’s Law
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Rules for Conductors
All excess charge within a conductor moves to its surface.
The electric field inside the material that makes up a conductor is zero.
Electric fields just outside the surface of a conductor are perpendicular to its surface.
Gauss’s Law is usually the best way to find the electric field of a conductor.
ElectricityElectric Flux and Gauss’s Law
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Q
E
24 rE
r
The electric flux
from Gauss’ Law
kQ4
The electric field
kQrE 44 2 2r
kQE
Outside any SphereA sphere with total charge Q
An imaginary Gaussian surface
ElectricityElectric Flux and Gauss’s Law
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Q
E
24 rE
r
The electric flux
Gauss’ Law
kQ4
The electric field
kQrE 44 2 2r
kQE
Outside any Spherical Shell
ElectricityElectric Flux and Gauss’s Law
9
Q
E
24 rE
r
The electric flux
Gauss’ Law
0
The electric field
04 2 rE 0E
Inside any Spherical Shell
R
0insideQ
ElectricityElectric Flux and Gauss’s Law
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For a cylinder or a plane, the principal is the same but the surface used changes
Note that the end faces must be included unless the cylinder is infinitely long.
En
En
ElectricityElectric Flux and Gauss’s Law
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q
Q
E
24 rE
r
The electric flux
Gauss’ Law
qQk 4
The electric field
qQkrE 44 2
2r
qQkE
Outside a Conductorwith a Point Charge Inside
ElectricityElectric Flux and Gauss’s Law
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q
Q
E
24 rE
r
The electric flux
Gauss’ Law
kq4
The electric field
kqrE 44 2 r
kqE
Inside a Conductorwith a Point Charge Inside
R
qQ inside
ElectricityElectric Flux and Gauss’s Law
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Q
q E
24 rE
r
The electric flux
Gauss’ Law
kQ4
The electric field
kQrE 44 2 2r
kQE
Outside a Conductorwith a Point Charge Outside
ElectricityElectric Flux and Gauss’s Law
14
Q
q E
24 rE
r
The electric flux
Gauss’ Law
04 k
The electric field
04 2 rE 0E
Inside a Conductor with a Point Charge Outside(it works as a shield and lets no electric field inside its walls)
R
0insideQ