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Gauss law aloe is not sufficient to determine the electric field for a given system.To determine electric field using Gauss law the symmetry of problem plays an important role by determining the direction of the electric field in given problem.
For several problems of computing electric field using Gauss law an important input is symmetry of the problem. The examples are well known. Here we collect commonly known examples of this type.Point charge
- Uniformly charged solid sphere
- Infinite line with uniform charge per unit length
- An infinite uniformly charged plane.
The symmetry of the problem determines the direction of the electric field and Gauss law can then be used to find the magnitude. A proof of direction of electric field is not written out in almost all text books. The reader is encouraged to think and write a proof.
In this context it is important to remember that Gauss law follows from the Coulomb's law, but the converse is not true. In other words, Gauss law is equivalent to the Maxwell's equation \(\nabla\cdot\vec E=\rho/\epsilon_0\) only. This equation alone does not imply Coulomb's law. To determine a vector field, knowledge of both its divergence and curl is necessary.
