w05d2 dielectrics catchup -...
TRANSCRIPT
Class 09 1
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W05D2 Dielectrics and Conductors as
Shields
Today’s Reading Assignment: Course Notes Sections 5.4, 5.6, 5.8-5.9
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
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Outline
Review: Stored Energy in Capacitors
Dielectrics
Electric Fields in Matter
Conductors as Shields
Class 09 2
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So change in stored energy to move dq is:
Total energy to charge to
Review: Stored Energy in Capacitor
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Energy stored in the E field!
Parallel-plate capacitor:
Energy density [J/m3]
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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
Class 09 3
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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. V, Q increases. 2. V increases, Q is the same. 3. V increases, Q decreases. 4. V is the same, Q increases. 5. V is the same, Q is the same. 6. V is the same, Q decreases. 7. V decreases, Q increases. 8. V decreases, Q is the same. 9. V decreases, Q decreases.
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Concept Q. Answer: Changing Dimensions
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 = E d
As d increases, V increases.
Answer: 2. V increases, Q is the same
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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.
Class 09 4
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Concept Q. Answer: Changing Dimensions
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.
Answer: 2. The stored energy increases
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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
Class 09 5
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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???
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Molecular View of Dielectrics
Polar Dielectrics :
Dielectrics with permanent electric dipole moments Example: Water
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Molecular View of Dielectrics
Non-Polar Dielectrics
Dielectrics with induced electric dipole moments Example: CH4
Class 09 6
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Dielectric in Capacitor
Potential difference decreases because dielectric polarization decreases Electric Field!
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Dielectric Constant Dielectric weakens original field by a factor
Dielectric constants Vacuum 1.0 Paper 3.7 Pyrex Glass 5.6 Water 80
Dielectric Constant
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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 is inserted between the plates. The charge stored in the capacitor
+ + + + + + + +
- - - - - - - -
1. Increases 2. Decreases 3. Stays the Same
Class 09 7
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Concept Question Answer: Dielectric
Since the capacitor is disconnected from a battery there is no way for the amount of charge on it to change.
Answer: 3. Charge stays the same
+ + + + + + + +
- - - - - - - -
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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 .
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Demonstration: Parallel Plate Capacitor
with Dielectric E5
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%205&show=0
Class 09 8
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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
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:
Answer: 2. Energy stored decreases
Class 09 9
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Dielectric in a Capacitor V0 = constant when battery remains connected
Upon inserting a dielectric free charge on plates increase
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Gauss’s Law with Dielectrics
κE ⋅dA
S∫∫ =
qfree,enc
ε0
In both cases:
This will be useful for homework problems
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Conductors as Shields
Class 09 10
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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. is initially uniform and does not change when the charge is moved.
2. is initially uniform but does become non-uniform when the charge is moved.
3. is initially non-uniform but does not change when the charge is moved.
4. is initially non-uniform but does change when the charge is moved.
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Concept Question Answer: Q in Conductor
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
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.
Demonstration:
Faraday Cage D33
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http://tsgphysics.mit.edu/front/?page=demo.php&letnum=D%2033&show=0
Class 09 11
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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
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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
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Experiment 1 Faraday Ice Cage
Class 09 12
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Demonstration: Dissectible Capacitor E2
Open Question: Think About
http://tsgphysics.mit.edu/front/?page=demo.php&letnum=E%202&show=0