Gauss Law

Gauss Law Gauss Law Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction. Gauss's law can be used to derive Coulomb's law, and vice versa.

What is Gauss Law? Note :- Gauss's law states that the enclosed electric charge in a closed surface is proportional to the net flux of an electric field through the surface.

The gauss law is one of the Maxwell law of electromagnetism and it relates to the electric fields at points on the Gaussian (closed) surface and the net charge enclosed by that surface.

The flux of the electric field passing through a closed surface is defined as the product of the electric field passing through the area and the area of the surface in a plane perpendicular to the field.

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In other words, Gauss law is also defined as the total charge Q enclosed within a surface divided by dielectric constant.

Gauss’s Law Examples :Now we will discuss few Gauss Law Examples to understand it better. For this we will now find the electric flux passing through sphere (also known as Gauss Law Sphere) and cylinder (also known as Gauss Law Cylinder) which nearly represents near Gaussian surfaces.

1) Electric flux for a sphere of uniform charges: Consider a sphere of radius R with charge Q distributed inside uniformly. For determining electric field E as a function of radius r of the sphere, we will use Gauss's law.

In the given figure below a spherical Gaussian surface of radius r is shown which are centered at the center of the spherical charge distribution.

The radius r of the spherical surface could be larger or could be smaller than the radius R of the spherical charge distribution.

For both the cases (r < R and R > r) we will find the electric field.

2) Electric flux for a cylinder of uniform charges: Let us consider a cylinder of infinite length. The electric field of such cylinder with the uniform volume charge density can also be obtained by using Gauss's law.

Considering a cylinder with radius r > R, the electric field is same magnitude at all points of the cylinder. This field is directed outward to the surface of the cylinder.

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Applying the integral form :- If the electric field is known everywhere, Gauss's law makes it quite easy, in principle, to find the distribution of electric charge: The charge in any given region can be deduced by integrating the electric field to find the flux.

However, much more often, it is the reverse problem that needs to be solved: The electric charge distribution is known, and the electric field needs to be computed. This is much more difficult, since if you know the total flux through a given surface, that gives almost no information about the electric field, which (for all you know) could go in and out of the surface in arbitrarily complicated patterns.

An exception is if there is some symmetry in the situation, which mandates that the electric field passes through the surface in a uniform way. Then, if the total flux is known, the field itself can be deduced at every point.

Common examples of symmetries which lend themselves to Gauss's law include cylindrical symmetry, planar symmetry, and spherical symmetry. See the article Gaussian surface for examples where these symmetries are exploited to compute electric fields.

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