Download - 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: ๐ถ=๐๐
๐=๐๐๐๐ ๐ก because V<V0
C>C0
ฮ := ๐ถ๐ถ0
=๐ 0
๐ K>1: relative dielectric constant
d
What happens with the E-field in the presence of dielectric material๐ธ=๐๐๐๐๐We know V<V0
E<E0 specifically ฮ=๐ 0
๐ =๐ธ0
๐ธ ๐ธ=๐ธ0
ฮ
Recall:
๐ธ0=๐๐0
๐ธ=๐โ๐ ๐
๐0and
๐ ๐=๐ (1โ 1๐พ ) ๐ธ=๐๐พ ๐0
๐=๐พ ๐0 Definition of the permittivity
and
The surface charge (density) ฯ on conducting plates does not change butinduced charge ฯi of opposite sign
๐ ๐๐๐กreduced with dielectric material
DIELECTRICSExample: K1
K2
d/2d/2
+Q
-Q
E0E1E2
โ๐ธ0โ=๐๐0
=๐๐0 ๐ด
โ๐ธ1โ=โ๐ธ0โ๐พ1
= ๐๐0๐ด ๐พ1
โ๐ธ2โ=โ๐ธ0โ๐พ2
= ๐๐0 ๐ด๐พ 2
V
๐ถ=๐๐ = ๐
๐๐2๐0 ๐ด
( 1๐พ 1+ 1๐พ 2
)=2๐0 ๐ด๐พ 1๐พ 2
๐ (๐พ 1+๐พ2)
๐ 1=๐ (1โ 1๐พ1
) ๐ 2=๐ (1โ 1๐พ 2
)
==
24.4 DIELECTRICSDielectric breakdown or Dielectric strength
Cr2 O3
Ground GroundHigh Voltage
Air
GAUSSโS LAW IN DIELECTRICSRecall:
Conductor Dielectrics๏ฟฝโ๏ฟฝ=0 ๏ฟฝโ๏ฟฝโ 0
๐โ๐ ๐
๐๐๐๐๐=(๐โ๐ ๐ ) ๐ด
โฎ๐ธ โ๐๐ด=๐ธ๐ด
AA
A
๐ธ๐ด=(๐โ๐ ๐ ) ๐ด
๐0
๐ ๐=๐ (1โ 1๐พ )
๐ธ๐ด=๐ ๐ด๐พ ๐0
๐๐๐๐๐โ ๐๐๐๐
๐0=โฎ๐พ ๐ธ โ ๏ฟฝโ๏ฟฝ๐ด
GAUSSโS LAW IN DIELECTRICSExample:Capacitance of half filled spherical capacitor
Kra
rbr
๐๐๐๐๐โ ๐๐๐๐
๐0=โฎ๐พ ๐ธ โ ๏ฟฝโ๏ฟฝ๐ด
๐๐0
=โฎ ๐พ ๏ฟฝโ๏ฟฝ โ ๏ฟฝโ๏ฟฝ๐ด=๐พ ๐ธ12๐๐2+๐ธ22๐๐ 2E1
E2
๐1
๐0๐2
๐0๐ธ1=
๐1
2๐0๐พ ๐๐ 2
๐ธ2=๐2
2๐0 ๐๐2
๐=โซ๐ ๐
๐ ๐
๐ธ1๐๐=๐1(๐๐โ๐ ๐)2๐0๐พ ๐ ๐๐๐ ๐
โโ๐1=ยฟ
2๐0๐พ ๐๐ ๐๐ ๐๐(๐ ๐โ๐๐)
ยฟ
๐=โซ๐ ๐
๐ ๐
๐ธ2๐๐=๐2(๐ ๐โ๐๐)2๐0 ๐๐๐ ๐๐
โโ๐2=
2๐0 ๐๐๐๐๐๐(๐ ๐โ ๐๐)
๐=๐1+๐2=2๐0๐ ๐๐๐ ๐๐
(๐๐โ๐ ๐)(๐พ +1)
๐ถ=๐๐ =
2๐0๐๐ ๐๐ ๐(๐พ +1)(๐ ๐โ๐๐)
Check: K->1 needs to reproduce empty =
MOLECULAR MODEL OF INDUCED CHARGE
EE
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 โinduced chargesโ. 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