Electric Field of a Spherical Charge and Gaussian Surfaces

This page can be used to assist the learning of Columb's law and Gauss' law in electrostatics.

(The above 3D model is built using VRML 2.0 and requires cosmoplayer plugin to view. Click here to enlarge.)

The red ball at the center is supposed to have a positive uniform spherical charge distribution. The blue ball is an imaginary probe with the associated arrow indicating the local electric field. It can be dragged to show the field at different locations. Two suggested Gaussian surfaces (a sphere and a cube) are provided and each of them can be put up by a mouse click. However, only the sphere is an useful choice.

This model may be used to understand the followings:

1. Electric field is a vector field. It has both a direction and a magnitude which depend on the position of observation, i.e. the location of the probe.
2. A Gaussian sphere allows the calculation of the magnitude of the electric field using Gauss's law. It is possible because the electric field is always parallel to the surface normal with its magnitude uniform everywhere on the surface.
3. A cube as a Gaussian surface does not allow a similar calculation. This is because the magnitude of the electric field and also the angle between the electric field and the surface normal are not constant on the cubic surface.