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## Example 4.1: Electric field of a uniformly charged sphere

Question: An insulating sphere of radius carries a total charge which is uniformly distributed over the volume of the sphere. Use Gauss' law to find the electric field distribution both inside and outside the sphere.

Solution: By symmetry, we expect the electric field generated by a spherically symmetric charge distribution to point radially towards, or away from, the center of the distribution, and to depend only on the radial distance from this point. Consider a gaussian surface which is a sphere of radius , centred on the centre of the charge distribution. Gauss' law gives where is the area of the surface, the radial electric field-strength at radius , and the total charge enclosed by the surface. It is easily seen that Thus, Clearly, the electric field-strength is proportional to inside the sphere, but falls off like outside the sphere.   Next: Electric Potential Up: Gauss' Law Previous: Worked Examples
Richard Fitzpatrick 2007-07-14