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100. (a) We use Gauss’ law to find expressions for the electric field inside and outside the
spherical charge distribution. Since the field is radial the electric potential can be written
as an integral of the field along a sphere radius, extended to infinity. Since different
expressions for the field apply in different regions the integral must be split into two parts,
one from infinity to the surface of the distribution and one from the surface to a point
inside. Outside the charge distribution the magnitude of the field is
E = q
/4
πε
0
r
2
and the
potential is
V = q
/4
πε
0
r
, where
r
is the distance from the center of the distribution. This is
the same as the field and potential of a point charge at the center of the spherical
distribution. To find an expression for the magnitude of the field inside the charge
distribution, we use a Gaussian surface in the form of a sphere with radius
r
, concentric
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 Spring '10
 Rebello,NobelS
 Charge, Electric Potential

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