Visualizing an Electric Field With HTML5 and WebGL, Part 2: Gaussian Surfaces

 Gauss's Law represents an important step in the quantitative understanding the electric fields that we have been drawing. Gauss's Law relates the integral of an electric field over a closed surface to the electric charge contained within that surface. As we will see, a well chosen surface will simplify the evaluation of this integral considerably.

A classic Gaussian surface example. The fields lines radiate
out from the charge and cross the Gaussian sphere.

Gauss's law relates the integral of an electric field over a closed surface to the electric charge contained within that surface. Just as the electric field is intrinsically three dimensional, the surfaces used in Gauss's law calculations are intrinsically three dimensional. Moreover, as the examples become more complex, and the efield library becomes more full featured, the roll of spatial symmetry will become more important. In these cases, the ability to interact with the visualizations will be still more important.

∯ S E ⋅ d A = 4 π q

Gauss's law is one of the next steps understanding electric fields and electric flux. The ability to visualize and manipulate Gaussian surfaces as well as the charge configuration aids a rapid understanding of the relationships among charges, fields and flux.

For example, a student can examine the visualization with the charge at the center of the Gaussian sphere1 and see that the electric field is constant and perpendicular to the surface, or parallel to d A

A charge outside of the Gaussian surface does not
contribute to the flux through the surface.

A second example illustrates how a charge outside of the Gaussian surface does not contribute to the total flux through the surface. Every field line that that crosses the Gaussian surface will cross the Gaussian surface again in the opposite direction.


Zero net charge within a Gaussian sphere.

A final example shows a balanced positive and negative charge within a Gaussian sphere so that the net charge within the sphere is zero. We can easily see that fields lines extend from the positive charge and cross the Gaussian surface. But these same field line cross back through the surface to yield no net flux.


1) The spherical geometry is based on the WebGL cookbook How to draw a sphere rescipe.
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