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Applications of Gauss's Law

In cases of high symmetry, Gauss's law may be readily used to calculate E. Otherwise it is not generally useful and integration over the charge distribution is required. But when the symmetry permits it, Gauss's law is the easiest way to go!

Gauss's Law

[Gauss's Law]

The CRUX OF ITS APPLICATION is the choice of gaussian surface. Keep in mind that this is not a surface of the charge distribution itself, but rather an imaginary surface constructed for application of Gauss's law.

To make Gauss's law tractable:

  1. All sections of the gaussian surface should be chosen so that they are either parallel or perpendicular to E. For this we need to have already determined the direction of E everywhere on the surface by symmetry arguments.
  2. |E| should be constant on each surface. Again, this requires sufficient symmetry to "see" the constancy of field strength.
And once again, make sure that the surface is closed!

Application of Gauss's Law to confirm "Coulomb's Law" for a Point Charge

[gaussian sphere]

Concept Check

Step-by-Step Example: Electric Field of Infinite Line of Charge by Gauss's Law

Step 1: Understand the geometry
Step 2: Understand the symmetry
Step 3: Construct the gaussian surface
Step 4: Examine the gaussian surface
Step 5: Evaluate the electric flux through the gaussian surface
Step 6: Evaluate the charge enclosed by the gaussian surface
Step 7: Apply Gauss's law for the result!

For Comparison: Infinite Line of Charge by Direct Integration

Another Example of Application of Gauss's Law: Non-Uniform Ball of Charge

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Last updated March 10, 1998.
Copyright George Watson, Univ. of Delaware, 1997.