W05D2
Dielectrics and Conductors as
Shields
Today s Reading Assignment:
Course Notes Sections 5.4, 5.6, 5.8-5.9
1
Announcements
Math Review Week 06 Tuesday 9-11 pm in 26-152
PS 5 due W05 Tuesday at 9 pm in boxes outside
32-082 or 26-152
Add Date Week 05 Friday
W05D3 Reading Assignment: Friday Problem Solving
Capacitance and Dielectrics
Course Notes Sections 5.6, 5.8-5.9
2
Outline
Review: Stored Energy in Capacitors
Dielectrics
Electric Fields in Matter
Conductors as Shields
3
Class 09
1
Review: Stored Energy in Capacitor
So change in stored energy to move dq is:
Total energy to charge to
4
Energy stored in the E field!
Parallel-plate capacitor:
Energy density [J/m3]
5
Demonstration:
Changing Distance Between
Circular Capacitor Plates E4
for Capacitor Disconnected to
Battery
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%204&show=0
6
Class 09
2
Concept Question: Changing Dimensions
A parallel-plate capacitor is charged until the plates have equal
and opposite charges ±Q, separated by a distance d, and then
disconnected from the charging source (battery). The plates
are pulled apart to a distance D > d. What happens to the
magnitude of the potential difference V and charge Q?
1.
2.
3.
4.
5.
6.
7.
8.
9.
V, Q increases.
V increases, Q is the same.
V increases, Q decreases.
V is the same, Q increases.
V is the same, Q is the same.
V is the same, Q decreases.
V decreases, Q increases.
V decreases, Q is the same.
V decreases, Q decreases.
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Concept Q. Answer: Changing Dimensions
Answer: 2. V increases, Q is the same
With no battery connected to the plates the charge on
them has no possibility of changing.
In this situation, the electric field doesn’t change when
you change the distance between the plates, so:
V=Ed
As d increases, V increases.
8
Concept Question: Changing Dimensions
A parallel-plate capacitor, disconnected from a battery,
has plates with equal and opposite charges, separated
by a distance d. Suppose the plates are pulled apart
until separated by a distance D > d. How does the final
electrostatic energy stored in the capacitor compare to
the initial energy?
1.  The final stored energy is smaller
2.  The final stored energy is larger
3.  Stored energy does not change.
9
Class 09
3
Concept Q. Answer: Changing Dimensions
Answer: 2. The stored energy increases
As you pull apart the capacitor plates you increase
the amount of space in which the E field is non-zero
and hence increase the stored energy. Where does
the extra energy come from? From the work you do
pulling the plates apart.
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Demonstration:
Show that when plates remain
connected to battery, potential
difference doesn’t change
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Capacitors and Dielectrics
12
Class 09
4
Dielectrics
A dielectric is a non-conductor or insulator
Examples: rubber, glass, waxed paper
When placed in a charged capacitor, the
dielectric reduces the potential difference
between the two plates
HOW???
13
Molecular View of Dielectrics
Polar Dielectrics :
Dielectrics with permanent electric dipole moments
Example: Water
14
Molecular View of Dielectrics
Non-Polar Dielectrics
Dielectrics with induced electric dipole moments
Example: CH4
15
Class 09
5
Dielectric in Capacitor
Potential difference decreases because
dielectric polarization decreases Electric Field!
16
Dielectric Constant
Dielectric weakens original field by a factor
Dielectric Constant
Dielectric constants
Vacuum
1.0
Paper
3.7
Pyrex Glass
5.6
Water
80
17
Concept Question: Dielectric
A parallel plate capacitor is charged to a total charge Q
and the battery removed. A slab of material with
dielectric constant
is inserted between the plates.
The charge stored in the capacitor
+ + + + + + + +
- - - - - - - -
1.  Increases
2.  Decreases
3.  Stays the Same
Class 09
18
6
Concept Question Answer: Dielectric
Answer: 3. Charge stays the same
+ + + + + + + +
- - - - - - - -
Since the capacitor is disconnected from a battery
there is no way for the amount of charge on it to
change.
19
Group Problem: Induced Surface Charge
Density
A dielectric material with constant
completely fills the space
between two conducting plates that have a surface charge
densities
as shown in the figure. Induced surface charge
densities
appear on the surfaces of the dielectric. Find an
expression for
in terms of
and
.
20
Demonstration:
Parallel Plate Capacitor
with Dielectric E5
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%205&show=0
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Class 09
7
Dielectric in a Capacitor
Q0 = constant after battery is disconnected
Upon inserting a dielectric free charge on plates does
not change, potential decreases, capacitance increases
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Concept Question: Dielectric
A parallel plate capacitor is charged to a total charge Q
and the battery removed. A slab of material with
dielectric constant
in inserted between the plates.
The energy stored in the capacitor
+ + + + + + + +
- - - - - - - -
1.  Increases
2.  Decreases
3.  Stays the Same
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Concept Question Answer: Dielectric
Answer: 2. Energy stored decreases
The dielectric reduces the electric field and hence
reduces the amount of energy stored in the field.
The easiest way to think about this is that the
capacitance is increased while the charge remains
the same so
Also from energy density:
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Class 09
8
Dielectric in a Capacitor
V0 = constant when battery remains connected
Upon inserting a dielectric free charge on plates increase
25
Gauss’s Law with Dielectrics
In both cases:
  qfree,enc

∫S∫ κ E ⋅ d A = ε 0
This will be useful for homework problems
26
Conductors as Shields
27
Class 09
9
Concept Question: Point Charge in Conductor
A point charge +Q is placed inside a
neutral, hollow, spherical conductor.
As the charge is moved around
inside, the surface charge density on
the outside
1.
2.
3.
4.
is initially uniform and does not change when the
charge is moved.
is initially uniform but does become non-uniform when
the charge is moved.
is initially non-uniform but does not change when the
charge is moved.
is initially non-uniform but does change when the
charge is moved.
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Concept Question Answer: Q in
Conductor
Answer: 1 is initially uniform and
does not change when the
charge is moved. The electric
outside is the field of a point
charge at the origin.
E = 0 in conductor  -Q on inner surface
Charge conserved  +Q on outer surface
E = 0 in conductor  No communication
between –Q & +Q  + Q uniformly distributed
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Demonstration:
Faraday Cage D33
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=D%2033&show=0
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Class 09
10
Shielding By Conducting Shell:
Applet Homework Problem
Charge placed INSIDE induces balancing charge ON
INSIDE. Electric field outside is field of point charge.
http://web.mit.edu/viz/EM/visualizations/electrostatics/ChargingByInduction/shielding/shielding.htm
31
Shielding by Conducting Shell:
Applet Homework Problem
Charge placed OUTSIDE induces charge separation
ON OUTSIDE. Electric field is zero inside.
http://web.mit.edu/viz/EM/visualizations/electrostatics/ChargingByInduction/shielding/shielding.htm
32
Experiment 1
Faraday Ice Cage
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Class 09
11
Demonstration:
Dissectible Capacitor E2
Open Question: Think About
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%202&show=0
34
Class 09
12