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Transcript
```W05D2
Dielectrics and Conductors as
Shields
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 32082 or 26-152
W05D3 Reading Assignment: Friday Problem Solving
Capacitance and Dielectrics
Course Notes Sections 5.6, 5.8-5.9
2
Outline
Dielectrics
Electric Fields in Matter
Conductors as Shields
3
Capacitors and Dielectrics
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???
5
Molecular View of Dielectrics
Polar Dielectrics :
Dielectrics with permanent electric dipole moments
Example: Water
6
Molecular View of Dielectrics
Non-Polar Dielectrics
Dielectrics with induced electric dipole moments
Example: CH4
7
Dielectric in Capacitor
Potential difference decreases because
dielectric polarization decreases Electric Field!
8
Dielectric Constant
Dielectric weakens original field by a factor
e = ke 0
E
k
E0

Dielectric Constant
Dielectric constants
Vacuum
1.0
Paper
3.7
Pyrex Glass
5.6
Water
80
9
Group Problem: Induced Surface Charge
Density
A dielectric material with constant k completely fills the space
between two conducting plates that have a surface charge
densities ±s as shown in the figure. Induced surface charge
densities ±s ind appear on the surfaces of the dielectric. Find an
expression for s ind in terms of k and s .
10
Demonstration:
Parallel Plate Capacitor
with Dielectric E5
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%205&show=0
11
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
V0
Q0
Q0
Q
V  C  

  C0

V V0 / 
V0
12
Dielectric in a Capacitor
V0 = constant when battery remains connected
Q  CV   C0V0
Upon inserting a dielectric free charge on plates increase
Q   Q0
13
Gauss’s Law with Dielectrics
In both cases:

E

d
A


S
qfree,in
0
14
Concept Questions:
Dielectric in a Capacitor
15
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 k is inserted between the plates.
The charge stored in the capacitor
+ + + + + + + +
k
- - - - - - - -
1. Increases
2. Decreases
3. Stays the Same
16
Answer: 3. Charge stays the same
+ + + + + + + +
k
- - - - - - - -
Since the capacitor is disconnected from a battery
there is no way for the amount of charge on it to
change.
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 k
in inserted between the
plates. The energy stored in the capacitor
+ + + + + + + +
k
- - - - - - - -
1. Increases
2. Decreases
3. Stays the Same
18
The dielectric reduces the electric field and hence
reduces the amount of energy stored in the field.
capacitance is increased while the charge remains
the same so
2
U  Q / 2C
Also from energy density:
2
 E
1
1
2
uE,0   0 E   0    uE ,0
2
2
 
 
19
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 k in inserted between the plates.
The force on the dielectric
+ + + + + + + +
k
- - - - - - - -
1. pulls in the dielectric
2. pushes out the dielectric
3. is zero
20
Answer: 1. The dielectric is pulled in
We just saw that the energy is reduced by the
introduction of a dielectric. Since systems want to
reduce their energy, the dielectric will be sucked into
the capacitor.
Alternatively, since opposing charges are induced
on the dielectric surfaces close to the plates, the
attraction between these will lead to the attractive
force.
21
Conductors as Shields
22
Concept Question:
Point Charge Inside Conductor
23
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.
24
Conductor
Answer: 1 is initially uniform and
does not change when the
charge is moved.
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
25
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 electric field outside
1.
2.
3.
4.
+Q
is zero and does not change
is non-zero but does not change
is zero when centered but changes
is non-zero and changes
26
Conductor
Answer: 2. is non-zero but does
not change.
E = 0 in conductor  -Q on inner surface
Charge conserved  +Q on outer surface
E = 0 in conductor  No “communication”
between –Q & +Q  + Q remains uniformly
distributed so E stays unchanged
27
Shielding By Conducting Shell:
Applet
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
28
Shielding by Conducting Shell:
Applet
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
29
Demonstration: