Physics 201- Introduction to Electricity & Magnetism
September 29- Applying Gauss' Law

How to calculate electric fields from a given charge distribution using Gaussí Law (rather than Coulombís Law & integration)

This procedure is basically taken from section 24-3 (page 429).

1. Determine if there is any symmetry to the given charge distribution.  If there is any symmetry, determine if it is one of the special cases that allows us to use Gauss' Law without having to integrate- planar, cylindrical or spherical.  If there isn't one of these three types of symmetry, then using Gauss' Law will be difficult and you might be better off using a different method.

2. Choose a Gaussian surface with the same symmetry as the charge distribution.  Choose the size of the surface such that the surface lies at the location where you want to determine the electric field.  With the proper choice of a Gaussian surface, the flux will easily be determined as the field will either be parallel or perpendicular to the normal vector.

3. Evaluate the integral,  ,which gives us the total flux through our surface.  Look for ways to simplify the integral by examining each surface of our Gaussian surface separately.  At this stage the electric field is still unknown, so leave it as simply E.

4. Determine the amount of charge enclosed by the Gaussian surface.  If the charge distribution is continuous you may have to integrate over the volume to find the total charge.

5. Now with Gauss' Law use your flux and enclosed charge to solve for the electric field.

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 Jeff Phillips phillips@lmu.edu Loyola Marymount University Fall 2002