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Gauss Law in Electrostatics

November 12, 2012

When a glass rod is rubbed with silk cloth, the charge accumulated on the glass rod is said to be positive and the charge accumulated on plastic rod rubbed which fur is said to be negative. When an ebonite rod is rubbed with fur, ebonite rod acquires negative charge and fur positive charge. These examples strongly suggest that the electric charges are not generated but acquired by transfer from one body to another. Electrification is the process by which a body gets charged.

Coulomb’s Law : The force of attraction or repulsion between two stationary electric charges is directly proportional to the product of the magnitudes of the two charges and is inversely proportional to the square of the distance between them. The force acts along the straight line joining the two charges.

Principle of superposition : If a charge ‘q’ is simultaneously acted upon by the electrical forces due to multiple charges q1 ,q2 ,q3 , ….qn ; then the net force acting on the charge is the vector sum of the individual forces acting on ‘a’ due to individual charges q1 , q2 , q3 , …..qn independently, each force acting at a time.
Electrostatics Gauss Laws :

By using Coulomb’s law and the superposition principle, we ca find electric field strength at a given point. But, in case of more complex configurations of charge, the electric field (E) can be more easily calculated by applying Gauss’s law of Gauss’s theorem.

Gauss’s law or Gauss’s theorem in Electrostatics states that ‘ the total electric flux through any closed surface is equal to `(1)/(epsi0)` times the net charge enclosed by the surface’. Here `epsi`0 is the permittivity of free space. Mathematically the Gauss’s law or Gauss’s theorem can be stated as

`oint` E.ds = q / `epsi`0 .

Here q is the total charge enclosed by the surface S. ‘`oint` ‘ denotes that the surface should be a closed surface enclosing a certain volume inside which the total charge is q.
Guass Laws

Guass’s law is quite useful in calculating the electric field in problems where it is possible to choose a closed surface such that the electric field (E) has a normal component which is either zero or has a single fixed value at every point on the surface . ( This is E.ds is equal to zero or has a fixed value) . Symmetry considerations in many problems make the application of Guass’s law much easier.

If there are no charges (or the net charge is zero) inside the closed surface evidently the electric flux `phi` = `oint` E.ds = 0. If the flux is positive, the net charge enclosed by the surface will be positive and if the flux is negative, the net charge enclosed by the surface is negative. The closed surface we construct (having symmetry considerations in view) to solve the given problem is called Gaussian surface.

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