1
Lecture 7
Chapter 16. Matter & Electric Fields
*
A Spherical Shell of Charge
*
A Solid Sphere Charged throughout its Volume
*
Integrating the Spherical Shell
Field inside:
Field outside:
E
=
1
4
πε
0
Q
r
2
ˆ
r
(like a point charge)
E
=
0
Electric Field of a Spherical Shell of Charge
We show both a
Qualitative approach
and
Integration approach
to demonstrate that the above result for the electric Feld inside
and outside a spherical shell of charge
E
1
+E
4
E
2
E
3
E
6
E
5
Divide into 6 areas:
Direction:
radial
 due to the symmetry
E
of a Sphere Outside
E
3
=
E
5
<
E
2
=
E
6
The y components of E
2
& E
6
and E
3
& E
5
cancel.
Only
components in the x direction
contribute to the Feld.
The net
electric Feld is radially
outward from the center of the
sphere.
*Can approximate the electric Feld as being caused by a point charge
with a charge equal to the total charge of the sphere.
Magnitude:
E
=
1
4
0
Q
r
2
How would a charged sphere interact with other charges?
 as a point charge (same force)
E
of a Sphere Outside
As long as we are far from a region of
distributed charges we can
approximate the electric field of that
region as being due to a point charge.
*The distance from location “A” to some regions is less than “r” & to other
regions greater than “r”.
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 Spring '07
 k
 Charge, Electric Fields

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