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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Chapter 28. Gauss’s Law
The nearly spherical shape
of the girl’s head determines
the electric field that causes
her hair to stream outward.
Using Guass’s law, we can
deduce electric fields,
particularly those with a
high degree of symmetry,
simply from the shape of the
charge distribution.
Chapter Goal: To
understand and apply
Gauss’s law.
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Topics:
• The Concept of Flux
• Gauss’s Law
• Conductors in Electrostatic Equilibrium
• Calculating Electric Flux
• Symmetry
• Using Gauss’s Law
Chapter 28. Gauss’s Law
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Chapter 28. Reading Quizzes
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The amount of electric field
passing through a surface is
called
A. Electric flux.
B. Gauss’s Law.
C. Electricity.
D. Charge surface density.
E. None of the above.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
The amount of electric field
passing through a surface is
called
A. Electric flux.
B. Gauss’s Law.
C. Electricity.
D. Charge surface density.
E. None of the above.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Gauss’s law is useful for calculating
electric fields that are
A. symmetric.
B. uniform.
C. due to point charges.
D. due to continuous charges.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Gauss’s law is useful for calculating
electric fields that are
A. symmetric.
B. uniform.
C. due to point charges.
D. due to continuous charges.
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Gauss’s law applies to
A. lines.
B. flat surfaces.
C. spheres only.
D. closed surfaces.
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Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.
Gauss’s law applies to
A. lines.
B. flat surfaces.
C. spheres only.
D. closed surfaces.
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The electric field inside a
conductor in electrostatic
equilibrium is
A. uniform.
B. zero.
C. radial.
D. symmetric.
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The electric field inside a
conductor in electrostatic
equilibrium is
A. uniform.
B. zero.
C. radial.
D. symmetric.
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Chapter 28. Basic Content and Examples
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The Electric Flux
The electric flux measures the amount of electric field
passing through a surface of area A whose normal to the
surface is tilted at angle from the field.
We can define the electric flux more concisely using the
dot-product:
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EXAMPLE 28.1 The electric flux inside a
parallel-plate capacitor
QUESTION:
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EXAMPLE 28.1 The electric flux inside a
parallel-plate capacitor
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EXAMPLE 28.1 The electric flux inside a
parallel-plate capacitor
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Tactics: Evaluating surface integrals
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The Electric Flux through a Closed Surface
The electric flux through a closed surface is
The electric flux is still the summation of the fluxes through
a vast number of tiny pieces, pieces that now cover a closed
surface.
NOTE: A closed surface has a distinct inside and outside.
The area vector dA is defined to always point toward the
outside. This removes an ambiguity that was present for a
single surface, where dA could point to either side.
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Gauss’s Law
For any closed surface enclosing total charge Qin,the net
electric flux through the surface is
This result for the electric flux is known as Gauss’s Law.
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Electrostatics of Conductors
Using the Gauss’ law, we can derive a set of important
properties about conductors in electrostatic
equilibrium.
(You may claim that you understand a little electrostatics
if you know all the following results. )
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Interior of Conductors in Electrostatic
Equilibrium
1. The electric field is zero at all points within aconductor in electrostatic equilibrium.Otherwise, the electric field would cause electrons to move and thus
violate the assumption that all the charges are at rest.
2. There can be no net charge inside any conductor inelectrostatic equilibrium.Otherwise, we construct a Gaussian surface around the region with
nonvanishing net charge, and we must have non-zero field on the
surface--in contradiction with result 1.
---> The inside of a conductor is completely “empty” asfar as electrostatics is concerned.
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Boundary of Conductors in Electrostatic
Equilibrium
3. All charges on a conductor must be distributed on its
surface: “surface charge”.
The electric field outside of conductor can be nonzero.
4. Right outside a conductor, the tangent component of
the field must be vanish: otherwise surface charge will
move.
--> The field on the conductor surface
must be perpendicular to the surface.
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The Normal Component of Field
at the outer-surface of Conductor
a). Construct a cylindrical Gaussian
surface and integrate the field over.
b). The flux through the inner disk and
side surface is clearly zero
c). The flux through the outer disk is
given by E A.
d). The total flux through the cylinder
Is given by the Gauss’ law.
5. The magnitude of electric field on the outer-surface of a
conductor is proportional to the surface charge density.
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Cavity inside a Conductor
In the presence of a cavity, again there can be no net charge
in the interior of a conductor.