# 24.4 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: πΆ0 =
With dielectric:
πΆ=
π
π0
π
π
Κ: =
π = ππππ π‘
πΆ
π0
=
πΆ0 π
because V&lt;V0
C&gt;C0
K&gt;1: relative dielectric constant
What happens with the E-field in the presence of dielectric material
πΈ = πππππ
πΈ0
π0 πΈ0
We know V&lt;V0
E&lt;E0 specifically
πΈ=
Κ=
=
Κ
π
πΈ
d
Recall: πΈ =
ππππ‘
π0
ππππ‘ reduced with dielectric
material
The surface charge (density) σ on
conducting plates does not change but
induced charge σi of opposite sign
π
πΈ0 =
π0
and πΈ =
π − ππ
π0
π
πΎπ0
1
ππ = π(1 − )
πΎ
πΈ=
π = πΎπ0
Definition of the
permittivity
π΄
1
πΆ = π π and π’ = 2 ππΈ 2
DIELECTRICS
+Q
Example:
E0
E1
E2
K1
K2
d/2
d/2
V
-Q
πΈ0
πΈ1
πΈ2
π
π
=
=
π0 π0 π΄
πΈ0
π
=
=
πΎ1
π0 π΄πΎ1
πΈ0
π
=
=
πΎ2
π0 π΄πΎ2
π1 = π(1 −
1
)
πΎ1
π2 π
π=
= 4π π΄
0
π0
1
= 4 (πΈ2 πΎ2 )2 πΎ +
1
1
ππ
2
π
π
+ πΈ2
2
2
π
π
π
ππ 1
1
=
+
=
( + )
π0 π΄πΎ1 π0 π΄πΎ2 2 2π0 π΄ πΎ1 πΎ2
V = πΈ1
π
π
2π0 π΄πΎ1 πΎ2
πΆ= =
=
ππ 1
1
π
( + ) π(πΎ1 + πΎ2 )
2π0 π΄ πΎ1 πΎ2
1
π2 = π(1 − )
πΎ2
1
πΎ1
1
πΎ2
1
π
1
π
+ πΎ πππ π’ = π΄π = 4π (π΄ )2
2
0
1
πΎ1
1
π
+ πΎ = 40 (πΈ1 πΎ1 )2
2
1
πΎ1
1
+πΎ
2
24.4 DIELECTRICS
Dielectric breakdown or Dielectric strength
High Voltage
Ground
Ground
Air
Cr2O3
GAUSS’S LAW IN DIELECTRICS
Recall:
πππππ
π0
=
πΈ β ππ΄
πΈ≠0
πΈ=0
Dielectrics
Conductor
πππππ = π − ππ π΄
πΈ β ππ΄ = πΈπ΄
πΈπ΄ =
π −ππ
π − ππ π΄
π0
1
ππ = π(1 − )
πΎ
πΈπ΄ =
ππ΄
πΎπ0
πππππ−ππππ
=
π0
A
A
A
πΎπΈ β ππ΄
GAUSS’S LAW IN DIELECTRICS
πππππ−ππππ
=
π0
Example:
K
E1
ra
r
rb
E2
π=
ππ
ππ
π=
ππ
ππ
π1 (ππ − ππ )
πΈ1 ππ =
2π0 πΎπππ ππ
πΈ2 ππ =
π2 (ππ − ππ )
2π0 πππ ππ
πΎπΈ β ππ΄
π
=
π0
πΎπΈ β ππ΄ = πΎπΈ1 2ππ 2 + πΈ2 2ππ 2
π2
π1
π0
π0
π1
πΈ1 =
2π0 πΎππ 2
π2
πΈ2 =
2π0 ππ 2
2π0 πΎπππ ππ π
π1 =
(ππ − ππ )
π2 =
2π0 πππ ππ π
(ππ − ππ )
2π0 πππ ππ π
π = π1 + π2 =
(πΎ + 1)
ππ − ππ
πΆ=
π 2π0 πππ ππ (πΎ + 1)
=
π
(ππ − ππ )
MOLECULAR MODEL OF INDUCED CHARGE
CLICKER QUESTION
A 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 = ο₯
C. A value depends on the material of the conductor
E
E0
ο½
ο³0 ο­ο³i
ο³0
ο½
1
K
8