### 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: 0 =
With dielectric:
=

0

Κ: =
=

0
=
0
because V<V0
C>C0
K>1: relative dielectric constant
What happens with the E-field in the presence of dielectric material
=
0
0 0
We know V<V0
E<E0 specifically
=
Κ=
=
Κ

d
Recall:  =

0
reduced with dielectric
material
The surface charge (density) σ on
conducting plates does not change but
induced charge σi of opposite sign

0 =
0
and  =
−
0

0
1
= (1 − )

=
= 0
Definition of the
permittivity

1
=   and  = 2  2
DIELECTRICS
+Q
Example:
E0
E1
E2
K1
K2
d/2
d/2
V
-Q
0
1
2

=
=
0 0
0

=
=
1
0 1
0

=
=
2
0 2
1 = (1 −
1
)
1
2
=
= 4
0
0
1
= 4 (2 2 )2  +
1
1

2

+ 2
2
2

1
1
=
+
=
( + )
0 1 0 2 2 20  1 2
V = 1

20 1 2
= =
=
1
1

( + ) (1 + 2 )
20  1 2
1
2 = (1 − )
2
1
1
1
2
1

1

+    =  = 4 ( )2
2
0
1
1
1

+  = 40 (1 1 )2
2
1
1
1
+
2
24.4 DIELECTRICS
Dielectric breakdown or Dielectric strength
High Voltage
Ground
Ground
Air
Cr2O3
GAUSS’S LAW IN DIELECTRICS
Recall:

0
=
∙
≠0
=0
Dielectrics
Conductor
=  −
∙  =
=
−
−
0
1
= (1 − )

=

0
−
=
0
A
A
A
∙
GAUSS’S LAW IN DIELECTRICS
−
=
0
Example:
K
E1
ra
r
rb
E2
=

=

1 ( −  )
1  =
20
2  =
2 ( −  )
20
∙

=
0
∙  = 1 2 2 + 2 2 2
2
1
0
0
1
1 =
20  2
2
2 =
20  2
20
1 =
( −  )
2 =
20
( −  )
20
= 1 + 2 =
( + 1)
−
=
20   ( + 1)
=

( −  )
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 = 
C. A value depends on the material of the conductor
E
E0

0 i
0

1
K
8
```