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

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Math Review Week 06 Tuesday 9-11 pm in 26-152

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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