introduction to dielectrics

8
Dielectrics Experiment: Place dielectrics between plates of capacitor at Q=const condition Observation: potential difference decreases to smaller value with dielectric material relative to air Without dielectric: With dielectric: = = because V<V 0 C>C 0 Κ := 0 = 0 K>1: relative dielectric constant

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24.4 Dielectrics. 24.6 Gauss’s law in dielectrics. 24.5 Molecular model of induced charge. Introduction to Dielectrics. 24.4 Dielectrics. d. Separate two metal sheet with small gap d. Increases the maximum possible potential difference between the capacitor plates. - PowerPoint PPT Presentation

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Page 1: Introduction to Dielectrics

Dielectrics

Experiment: Place dielectrics between plates of capacitor at Q=const condition

Observation: potential difference decreases to smaller value with dielectric material relative to air

Without dielectric:

With dielectric: 𝐶=𝑄𝑉

𝑄=𝑐𝑜𝑛𝑠𝑡 because V<V0

C>C0

Κ := 𝐶𝐶0

=𝑉 0

𝑉 K>1: relative dielectric constant

Page 2: Introduction to Dielectrics

d

What happens with the E-field in the presence of dielectric material𝑸=𝒄𝒐𝒏𝒔𝒕We know V<V0

E<E0 specifically Κ=𝑉 0

𝑉 =𝐸0

𝐸 𝐸=𝐸0

Κ

Recall:

𝐸0=𝜎𝜖0

𝐸=𝜎−𝜎 𝑖

𝜖0and

𝜎 𝑖=𝜎 (1− 1𝐾 ) 𝐸=𝜎𝐾 𝜖0

𝜖=𝐾 𝜖0 Definition of the permittivity

and

The surface charge (density) σ on conducting plates does not change butinduced charge σi of opposite sign

𝜎 𝑛𝑒𝑡reduced with dielectric material

Page 3: Introduction to Dielectrics

DIELECTRICSExample: K1

K2

d/2d/2

+Q

-Q

E0E1E2

‖𝐸0‖=𝜎𝜖0

=𝑄𝜖0 𝐴

‖𝐸1‖=‖𝐸0‖𝐾1

= 𝑄𝜖0𝐴 𝐾1

‖𝐸2‖=‖𝐸0‖𝐾2

= 𝑄𝜖0 𝐴𝐾 2

V

𝐶=𝑄𝑉 = 𝑄

𝑄𝑑2𝜖0 𝐴

( 1𝐾 1+ 1𝐾 2

)=2𝜖0 𝐴𝐾 1𝐾 2

𝑑 (𝐾 1+𝐾2)

𝜎 1=𝜎 (1− 1𝐾1

) 𝜎 2=𝜎 (1− 1𝐾 2

)

==

Page 4: Introduction to Dielectrics

24.4 DIELECTRICSDielectric breakdown or Dielectric strength

Cr2 O3

Ground GroundHigh Voltage

Air

Page 5: Introduction to Dielectrics

GAUSS’S LAW IN DIELECTRICSRecall:

Conductor Dielectrics�⃗�=0 �⃗�≠0

𝜎−𝜎 𝑖

𝑄𝑒𝑛𝑐𝑙=(𝜎−𝜎 𝑖 ) 𝐴

∮𝐸 ∙𝑑𝐴=𝐸𝐴

AA

A

𝐸𝐴=(𝜎−𝜎 𝑖 ) 𝐴  

𝜖0

𝜎 𝑖=𝜎 (1− 1𝐾 )

𝐸𝐴=𝜎 𝐴𝐾 𝜖0

𝑄𝑒𝑛𝑐𝑙− 𝑓𝑟𝑒𝑒

𝜖0=∮𝐾 𝐸 ∙ �⃗�𝐴

Page 6: Introduction to Dielectrics

GAUSS’S LAW IN DIELECTRICSExample:Capacitance of half filled spherical capacitor

Kra

rbr

𝑄𝑒𝑛𝑐𝑙− 𝑓𝑟𝑒𝑒

𝜖0=∮𝐾 𝐸 ∙ �⃗�𝐴

𝑄𝜖0

=∮ 𝐾 �⃗� ∙ �⃗�𝐴=𝐾 𝐸12𝜋𝑟2+𝐸22𝜋𝑟 2E1

E2

𝑄1

𝜖0𝑄2

𝜖0𝐸1=

𝑄1

2𝜖0𝐾 𝜋𝑟 2

𝐸2=𝑄2

2𝜖0 𝜋𝑟2

𝑉=∫𝑟 𝑎

𝑟 𝑏

𝐸1𝑑𝑟=𝑄1(𝑟𝑏−𝑟 𝑎)2𝜖0𝐾 𝜋 𝑟𝑎𝑟 𝑏

❑⇒𝑄1=¿

2𝜖0𝐾 𝜋𝑟 𝑎𝑟 𝑏𝑉(𝑟 𝑏−𝑟𝑎)

¿

𝑉=∫𝑟 𝑎

𝑟 𝑏

𝐸2𝑑𝑟=𝑄2(𝑟 𝑏−𝑟𝑎)2𝜖0 𝜋𝑟𝑎 𝑟𝑏

❑⇒𝑄2=

2𝜖0 𝜋𝑟𝑎𝑟𝑏𝑉(𝑟 𝑏− 𝑟𝑎)

𝑄=𝑄1+𝑄2=2𝜖0𝜋 𝑟𝑎𝑟 𝑏𝑉

(𝑟𝑏−𝑟 𝑎)(𝐾 +1)

𝐶=𝑄𝑉 =

2𝜖0𝜋𝑟 𝑎𝑟 𝑏(𝐾 +1)(𝑟 𝑏−𝑟𝑎)

Check: K->1 needs to reproduce empty =

Page 7: Introduction to Dielectrics

MOLECULAR MODEL OF INDUCED CHARGE

EE

Page 8: Introduction to Dielectrics

8

CLICKER QUESTIONA conductor is an extreme case of a dielectric, since if an electric field is applied to a conductor, charges are free to move within the conductor to set up “induced charges”. What is the dielectric constant of a perfect conductor?

A. K = 0

B. K =

C. A value depends on the material of the conductor

0

0 0

1iEE K