If I bring a charged rod to a leaf electrometer: A] nothing will happen B] nothing will happen until I touch the electrometer with the rod - then the leaves will spread apart C] the leaves will spread apart when I get the rod close to the electrometer

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• Real Insulators (Dielectrics)

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If I bring a charged rod to a leaf
electrometerA nothing will happenB nothing
will happen until I touch the electrometer with
the rod - then the leaves will spread apartC
the leaves will spread apart when I get the rod
close to the electrometer
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What is the direction of the electric force on a
negative charge at 1? B A to the rightB to
the leftC upD down
What is the direction of the electric force on a
positive charge at 2? B
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If I put a charge at 3., what is the direction
of the electric force?A straight down,
directly toward the - chargeB straight
up,directly away from the - chargeC a little
to the right from straight downD a little to
the left from straight down
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What could be the charges here?Assume that all
field lines are shown. A Q1 3C, Q2 -2
CB Q1 18C, Q2 -10 CC Q1 -18C, Q210
CD Q1 9 C, Q2 5 CE none of these
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Electric field is defined by the force on a test
charge. Since forces add by superposition,
fields do also.
Field lines

• Field lines never cross each other
• Field lines are perpendicular to conductors at
  their surfaces
• Field lines share the symmetry of the sources
  sinks
• Density of field lines (in 3D) is proportional to
  field strength

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Which picture shows the field lines from an
infinite sheet containing a uniformly dense
negative charge? D
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What is wrong with picture B?
A field lines are symmetric top/bottom B field
lines cross C field lines are symmetric
right/left D field lines should start at sheet
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What figure shows the E field lines for an
electric dipole? B
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Whats wrong with Figure C?
A it has the wrong symmetry B it has the wrong
direction of field lines C field lines have
sharp turns
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Two source charges have equal magnitude. One is
and the other -, as shown. What vector could
represent the electric field at the point shown
caused BY THE POSITIVE CHARGE ALONE? B
Given that B is the field from the charge
alone, what vector could be the total field from
both charges? C
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If charge 3q is changed to -3q, what is the
direction of the total E field at p? A upward
and to the left B straight to the left C
downward and to the left D straight downward E
the E fields from q and -3q perfectly cancel
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Calculus how do we find E fields from extended
charge distributions?
Use symmetry Apply Coulombs Law to infinitesimal
parts Take components Use calculus to sum up all
contributions for either the x or the y
component
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Two plates extend the same distance into the
page. Their heights, projected onto the vertical
axis, are the same.What is the area of plate 2,
compared with the area of plate 1?
?
A same B C D
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If the dot product of E and the area of plate 1
is EA1, what is the dot product of E and the area
of plate 2?
?
?
A same B C D
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What would happen to the flux if we were to
double the field?
?
?
A same B double C half D quadruple
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The flux is proportional to the field, and to the
perpendicular area.We know the density of field
lines (lines per perpendicular area) is
proportional to the field.
?
?
So the flux is proportional to the number of
field lines penetrating a surface area. Note
the sign depends on how we orient the surface!
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Does the total flux through a spherical surface
at radius R change if we move the charge
off-center?

• A yes
• B no

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Does the total flux through a closed surface
surrounding a point charge change is we distort
the surface (while keeping it closed)?

• A yes
• B no

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Gauss Law is useful for finding E fields when
there is symmetry. Sphere of chargeLine of
chargeSheet of chargeGauss law also shows
that excess charge on a conductor is all at the
surface!
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A small sphere and a short rod have the same
charge Q. Gauss Law allows us to conclude that
the electric field a distance r away from each
(if looked at separately) would be the same.

• A True
• B False

FALSE! There is not enough symmetry to use Gauss
with the finite rod!!!!!!
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What is the charge on the inner surface of the
conducting shell?

• A 0
• B Q
• C -Q
• D 2Q
• E cannot determine

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If I put no excess charge on the conductor, the
net charge on its inner surface will bea
0b Qc -Qd -2Qe cannot determine
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Because there is zero E field in a conductor, the
inner surface must hold a charge -Q. What is
the charge on the outer surface?a 0b Qc
-Qd -2Qe cannot determine
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With no net charge on the outer conductor, the
inner surface gets -Q and so the outer surface
gets Q. Suppose, instead, I put 8Q on the
outer conductor. What then is the charge on its
inner surface?a 0b Qc -Qd 3Qe 4Q
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There still must be no field in the conductor. So
the inner surface is still -Q. Thus, the outer
surface will have 9Q, so that the total is 8Q
(9Q - 1Q).Given the peanut shaped geometry
and the fact that the charge Q is off-center, is
the charge density on the inner surface uniform
(the same everywhere on that surface)?a
yesb no
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The negative charge on the inner surface will be
concentrated close to the positive charge. (The E
field next to the surface is stronger there
!)If there is 9Q of charge on the outer
surface, will the charge density on the outer
surface be uniform?a yesb no
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There is no electric field in the conductor. So
the outside of the conductor cannot know that
there is an off-center charge in the middle!So
the charge density on the outer surface is
uniform. a yes