Transcript Day 4: Dielectrics & Their Molecular Description

Day 4: Dielectrics & Their Molecular
Description
• Definition of dielectric material
• Effects of the presence of dielectric material
in a capacitor
• The electric field between capacitor plates in
the presence of a dielectric
• Molecular description of dielectrics
Dielectrics
• Any insulating material placed between the
plates of a capacitor is called a dielectric
• Ex: paper, Mylar, mica, oil, ceramic
Effects of the Presence of a Dielectric
• The presence of a dielectric material
increases the capacitance of the capacitor
A
C  C0  0
where 0   permittivi ty
d
•  is the dielectric constant
• The energy density stored in the electric is
now:
2
2
1
1
  2 0 E  2 E
Dielectric Constants of Various
Materials
• The dielectric strength is
the maximum electric field
before breakdown
Effect of the Electric Field when a
Dielectric is Inserted
• The electric field in the presence of
1
a dielectric is reduced by a factor of:

• With no dielectric:
E0 
V0
d
V V0
E0
or ED 
• With a dielectric: E  ED  
d d

• The potential difference drops to: V 
V0

Molecular Description of Dielectrics
• An air dielectric capacitor C0, charged to ΔV0,
produces charges ±Q on each plate.
Q  C0  V0
Molecular Description of Dielectrics
• If the capacitor is isolated E0  d  V0 and a
dielectric is inserted, the charge Q is
unchanged
Molecular Description of Dielectrics
• When the dielectric is inserted,
the electric field between the plates
causes the molecules of the
insulator to become polarized
• Some of the electric field lines
do not pass thru the dielectric but
rather end on the induced charges
on the surface of the dielectric
Molecular Description of Dielectrics
• The electric field is weaker than
in air by: 1

• ΔV across the capacitor is also
reduced by: 1

• Since Q  C  V capacitance must increase
Molecular Description of Dielectrics
• The electric field within the
dielectric can be treated as the
vector sum of the electric field
due to the free charges on the
plates E0 and the electric field
due to the induced charges on the surface of
E0
the dielectric Eind
E  E   E  
D
 Eind
0
ind

 1
 E0 
 E0 1  

 
E0
Consequences of Dielectrics
• Remember that the electric field between the plates is
related to the surface charge density σ
If E0 

0
then Eind 
  ind
where  
Q
A
 ind
Q
where  ind  ind
0
A
1

  1  
 
and Qind
1

 Q 1  
 
• The induced charge on the dielectric is always less than
the free charge on the capacitor plates