Chapter 34
Gauss’s Law Example
304
34
Gauss’s Law Example
We finished off the last chapter by using Gauss’s Law to find the electric field due to a point
charge.
It was an example of a charge distribution having spherical symmetry.
In this chapter
we provide another example involving spherical symmetry.
Example 341
Find the electric field due to a uniform ball of charge of radius
R
and total charge
Q
.
Express
the electric field as a function of
r
, the distance from the center of the ball.
Solution
Again we have a charge distribution for which a rotation through any angle about any axis
passing through the center of the charge distribution results in the exact same charge
distribution.
Thus, the same symmetry arguments used for the case of the point charge apply
here with the result that, the electric field due to the ball of charge has to be strictly radially
directed, and, the electric field has one and the same value at every point on any given
spherical shell centered on the center of the ball of charge.
Again, we assume the electric
field to be outwarddirected.
If it turns out to be inwarddirected, we’ll simply get a negative
value for the magnitude of the outwarddirected electric field.
Charge
Q
, uniformly
distributed throughout
a spherical region (
a
solid ball of charge
)
of radius
R
.
E
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Chapter 34
Gauss’s Law Example
305
o
ENCLOSED
e
Q
dA
E
=
The appropriate Gaussian surface for any spherical charge distribution is a spherical shell
centered on the center of the charge distribution.
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 Fall '08
 RABE
 Physics, Charge, Electrostatics, Electric charge, Fundamental physics concepts, gaussian surface

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