Gauss’s Law
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What is Gauss’s law all about?: |
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The Gauss’s law is a law which describes how to calculate the electric field in an alternative
manner. It is based on the fact that the fundamental electrostatic force between point charges
exhibits an inverse-square behavior. It is a consequence of Coulomb’s law. However, this law is
more convenient for calculating the electric fields of highly symmetric charge distributions. It also
helps in providing the possible useful qualitative reasoning while dealing with complicated
problems.
The flux of a vector field:
a surface of area A which is perpendicular to the field. The number of lines per unit area is
proportional to the magnitude of the electric field. Therefore, the total number of lines penetrating
the surface is proportional to the product EA. This product of the magnitude of electric field E and
surface area A perpendicular to the field is called the electric flux:
Electric flux is proportional to the number of electric field lines penetrating some surface.
if the surface under consideration is not perpendicular to the field, the flux through it must be
less than the given equation as above. If the surface makes an angle of θ with the electric field
then the flux is given by,
In a more general manner, the electric field may vary over a surface. Then, the flux can be
given by,
This integral is a surface integral and is integrated over a surface. If the surface under
consideration is a closed surface then the electric flux is given
by,
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