1) Gauss's law relates the electric flux passing through a closed surface to the electric charge enclosed by the surface. It states that the total electric flux is proportional to the total enclosed charge. 2) Gauss's law is useful for calculating electric fields of highly symmetric charge distributions. It allows choosing a Gaussian surface where the surface integral can be easily evaluated. 3) When a conductor is in electrostatic equilibrium, the electric field inside is zero. Any charges reside on the surface of the conductor. The electric field just outside the conductor is perpendicular to the surface with a magnitude proportional to the surface charge density.

1. ELECTRIC FLUX
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2. Electric Flux
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3. Electric Flux
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4. Electric Flux, Interpreting the
Equation
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5. Electric Flux, cont.
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6. Gauss’s Law, Introduction
•Gauss’s law is an alternative to coulomb’s law for expressing
the relationship between electric charge and electric field.
•It states that the total electric flux out of any closed surface
is proportional to the total electric charge inside the surface.
 The closed surface is often called a gaussian surface.
•Gauss’ Law is based on the inverse-square behavior of the
electric force between point charges.
•It is convenient for calculating the electric field of highly
symmetric charge distributions.
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7. Gauss’s Law – Cont.
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8. Gaussian Surface, Example
•Closed surfaces of various shapes can
surround the charge.
• Only S1 is spherical
•Verifies the net flux through any closed
surface surrounding a point charge q is
given by q/eo and is independent of the
shape of the surface.
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9. Gaussian Surface, Example 2
•The charge is outside the closed
surface with an arbitrary shape.
•Any field line entering the surface
leaves at another point.
•Verifies the electric flux through a
closed surface that surrounds no
charge is zero.
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10. Gauss’s Law – cont.
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11. Gauss’s Law – General, notes
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12. Applying Gauss’s Law
•To use Gauss’s law, you want to choose a gaussian
surface over which the surface integral can be simplified
and the electric field determined.
•Take advantage of symmetry.
•Remember, the gaussian surface is a surface you
choose, it does not have to coincide with a real surface.
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14. Properties of a Conductor in
Electrostatic Equilibrium
•When there is no net motion of charge within a conductor, the
conductor is said to be in electrostatic equilibrium.
•The electric field is zero everywhere inside the conductor.
• Whether the conductor is solid or hollow
•If the conductor is isolated and carries a charge, the charge resides on
its surface.
•The electric field at a point just outside a charged conductor is
perpendicular to the surface and has a magnitude of σ/εo.
• s is the surface charge density at that point.
•On an irregularly shaped conductor, the surface charge density is
greatest at locations where the radius of curvature is the smallest.
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15. Property 1: Fieldinside = 0
•Consider a conducting slab in an
external field.
•If the field inside the conductor
were not zero, free electrons in the
conductor would experience an
electrical force.
•These electrons would accelerate.
•These electrons would not be in
equilibrium.
•Therefore, there cannot be a field
inside the conductor.
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16. Property 1: Fieldinside = 0, cont.
•Before the external field is applied, free electrons are distributed
throughout the conductor.
•When the external field is applied, the electrons redistribute until
the magnitude of the internal field equals the magnitude of the
external field.
•There is a net field of zero inside the conductor.
•This redistribution takes about 10-16 s and can be considered
instantaneous.
•If the conductor is hollow, the electric field inside the conductor
is also zero.
• Either the points in the conductor or in the cavity within the
conductor can be considered.
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17. Property 2: Charge Resides on the
Surface
•Choose a gaussian surface inside
but close to the actual surface.
•The electric field inside is zero
(property 1).
•There is no net flux through the
gaussian surface.
•Because the gaussian surface can
be as close to the actual surface as
desired, there can be no charge
inside the surface.
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18. Property 2: Charge Resides on the
Surface, cont.
•Since no net charge can be inside the surface, any net
charge must reside on the surface.
•Gauss’s law does not indicate the distribution of these
charges, only that it must be on the surface of the
conductor.
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19. Property 3: Field’s Magnitude and
Direction
•Choose a cylinder as the Gaussian
surface.
•The field must be perpendicular
to the surface.
• If there were a parallel component
to , charges would experience a
force and accelerate along the
surface and it would not be in
equilibrium.
E
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20. Property 3: Field’s Magnitude and
Direction, cont.
•The net flux through the gaussian surface is through
only the flat face outside the conductor.
• The field here is perpendicular to the surface.
•Applying Gauss’s law
E
o o
σA σ
EA and E
ε ε
   
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21. Example 1-Electric flux
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22. Example 2-Electric flux
In the following figure, a
butterfly net is in a uniform
electric field of magnitude
E =3 mN/C. the rim of
radius a= 11 cm, is aligned
perpendicular to the field.
If the net contains no net
charge,
find the electric flux
through the netting
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23. Example 3-Gauss’s law
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24. Example 4-Gauss’s law
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25. Electrostatic shielding – Faraday’s cage
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26. Faraday cage-Example.
• It is useful when one wants to protect
sensitive equipment from stray fields
that might affect measurements, and can
also protect against dangerous electric
discharge. Examples of this are:
measuring equipment surrounded by
aluminium foil or copper;
and in a thunderstorm a car can act as a
Faraday cage and protect from
dangerous electric discharge.
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