93
Chapter 22
The Electric Field 2: Continuous Charge
Distributions
Conceptual Problems
1
•
[SSM]
Figure 2237 shows an Lshaped object that has sides that are
equal in length.
Positive charge is distributed uniformly along the length of the
object. What is the direction of the electric field along the dashed 45
o
line?
Explain your answer.
Determine the Concept
The resultant field is the superposition of the electric
fields due to the charge distributions along the axes and is directed along the
dashed line, pointing away from the intersection of the two sides of the Lshaped
object. This can be seen by dividing each leg of the object into 10 (or more) equal
segments and then drawing the electric field on the dashed line due to the charges
on each pair of segments that are equidistant from the intersection of the legs.
2
•
Positive charge is distributed uniformly along the entire length of the
x
axis, and negative charge is distributed uniformly along the entire length of the
y
axis.
The charge per unit length on the two axes is identical, except for the sign.
Determine the direction of the electric field at points on the lines defined by
y
=
x
and
y
= –
x
. Explain your answer.
Determine the Concept
The electric fields along the lines defined by
y
=
x
and
y
= –
x
are the superposition of the electric fields due to the charge distributions
along the axes. The direction of the electric field is the direction of the force
acting on a test charge at the point(s) of interest. Typical points are shown at two
points on each of the two lines.
x
y
x
y
=
−
+
+
+
+
+
+
+
+
−
−
−
−
−
−
−
−
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94
3
•
True or false:
(
a
)
The electric field due to a hollow uniformly charged thin spherical shell is
zero at all points inside the shell.
(
b
)
In electrostatic equilibrium, the electric field everywhere inside the material
of a conductor must be zero.
(
c
)
If the net charge on a conductor is zero, the charge density must be zero at
every point on the surface of the conductor.
(
a
) True (assuming there are no charges inside the shell).
(
b
) True. The charges reside on the surface of conductor.
(
c
) False. Consider a spherical conducting shell. Such a surface will have equal
charges on its inner and outer surfaces but, because their areas differ, so will their
charge densities.
4
•
If the electric flux through a closed surface
is zero, must the electric
field be zero everywhere on that surface? If not, give a specific example. From the
given information can the net charge inside the surface be determined? If so, what
is it?
Determine the Concept
No, this is not necessarily true. The only conclusion that
we can draw is that there is equal positive and negative flux. For example, the net
flux through a Gaussian surface completely enclosing a dipole is zero. If the
electric flux is zero through the closed surface, we can conclude that the net
charge inside the surface is zero.
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 Spring '12
 Goussiou
 Physics, Charge, The Land

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