Monday, August 8, 2011

How to use Gauss's Law to find electric field

W all know that Gauss's law is basically the relation between the charge distribution producing the electrostatic field to the behaviour of electrostatic field in space. Also Gauss's law is based on the fact that flux through any closed surface is a measure of total amount of charge inside that surface and any charge outside that surface would not contribute anything to the total flux. Now we'll go through the main steps which we can employ for applying Gauss's Law

1. First identify the symmetry properties of the charge distribution. By this we mean that the point at which the field is to be determined must lie on a surface and this surface must have enough symmetry which allows integrals involved to be evaluated properly.
2. Determine the direction of the electric field and a surface on which the magnitude of electric field is constant.
3. Now choose the Gaussian surface accordingly for example if the problem has spherical symmetry then Gaussian surface would usually be spherical and for cylindrical symmetry problem Gaussian surface would be cylindrical.
4. Calculate the flux through the Gaussian surface.
5. Now calculate the charge enclosed inside the chosen Gaussian surface.
6. Equate the two sides of Gauss's law in order  to find the expression for the magnitude of the electric field in that region of space.