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*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