Definitions

• Dielectric—an insulating material placed between plates of a capacitor to increase capacitance.

• Dielectric constant—a dimensionless factor that determines how much the capacitance is increased by a dielectric. It is a property of the dielectric and varies from one material to another.

• Breakdown potential—maximum potential difference before sparking

• Dielectric strength—maximum E field before dielectric breaks down and acts as a conductor between the plates (sparks)

Most capacitors have a non-conductive material (dielectric) between the conducting plates. That is used to increase the capacitance and potential across the plates.

Dielectrics have no free charges and they do not conduct electricity

Faraday first established this behavior

Capacitors with Dielectrics

• Advantages of a dielectric include:1. Increase capacitance

2. Increase in the maximum operating voltage. Since dielectric strength for a dielectric is greater than the dielectric strength for air

3. Possible mechanical support between the plates which decreases d and increases C.

• To get the expression for anything in the presence of a dielectric you replace o with o

airdiairdi VVEE maxmaxmaxmax

00; decreases: /

k SC V Ed E E E k

d

Field inside the capacitor became smaller – why?

There are polarization (induced) charges

– Dielectrics get polarized

We know what happens to the conductor in the electric field

Field inside the conductor E=0outside field did not change

Potential difference (which is the integral of field) is, however, smaller.

( )o

V d b

0

[1 / ]

AC

d b d

Properties of Dielectrics

0EEK

Redistribution of charge – called polarization

We assume that the induced charge is directly proportional to the E-field in the material

0

CK

C dielectric constant of a material

0VVK

when Q is kept constant

In dielectrics, induced charges do not exactly compensate charges on the capacitance plates

00 0

; iE E

1

1i K

Induced charge density

0K Permittivity of the dielectric material

E

E-field, expressed through charge density on the conductor plates (not the density of induced charges) and permittivity of the dielectric (effect of induced charges is included here)

21

2u E Electric field density in the dielectric

Example: A capacitor with and without dielectric

Area A=2000 cm2

d=1 cm; V0 = 3kV;

After dielectric is inserted, voltage V=1kV

Find; a) original C0 ; b) Q0 ; c) C d) K e) E-field

Dielectric Breakdown

Dielectric strength is the maximum electric field the insulator can sustain before breaking down

Plexiglas breakdown

Applications

In 1995, the microprocessor unit on the microwave imager on the DMSP F13 spacecraft locked up - occurred ~5 s after spacecraft began to charge up in the auroral zone in an auroral arc. Attributed to high-level charging of spacecraft surface and subsequent discharge.

Thermal blankets - composed of layers of dieletric material with vapor deposited aluminum (VDA) between each layer. On DMSP, VDA between layers (22) not grounded - serve as plates of a set of 22 parallel-plate capacitors - top plate consists of electrons buried in top few microns of Teflon.

Spacecraft surfaces are generally covered with thermal blankets - outer layer some dielectric material - typically Kapton or Teflon. Deposition of charge on surface of spacecraft known as surface charging. Incident electrons below about 100 keV penetrate the material to a depth of a few microns, where they form a space charge layer - builds up until breakdown occurs accompanied by material vaporization and ionization. A discharge is initiated - propagates across surface or through the material, removing part of bound charge. Typically occur in holes, seams, cracks, or edges - have been know to seriously damage spacecraft components.

€

1

C=

1

c ii=1

22

∑

C/A=7.310-9 F/m2

Time to charge outer surface of a parallel plate capacitor to some voltage with respect to spacecraft frame is:

t=CV

i(1−δ)A

Laboratory measurements for Teflon:

-discharge at 3 kV in a 20 keV electron beam-secondary electron yield () at 20 keV ~ 0.2

Given measured incident precipitating current density of i = 4.8 A/m2, the time to reach breakdown voltage for conditions experienced by DMSP F13 is 5.7 s - this is the time after the spacecraft began to charge up that the lockup occurred.

If the VDA layer on the bottom side of the outer Teflon layer were grounded to the spacecraft frame, the capacitance would have been 3.510-7 F/m2 and the charging time would have been 132 s - no discharge would have occurred.

Molecular Model of Induced ChargeElectronic polarization of nonpolar molecules

tom)molecule/a a oflity polarizabi theis (

:field in themoment dipole finite acquire

but they field electric applied theof

absence in the 0 moleculesnonpolar For

ngnonvanishi bemay moment dipoleBut

0 charge Total

0

Ed

E

d

rd

ii

i

ii

q

qQ

In the electric field more molecular dipoles are oriented along the field

Electronic polarization of polar molecules

Polarizability of an Atom

- separation of proton and electron cloud in the applied electric field

P- dipole moment per unit volume, N – concentration of atoms

0

When per unit volume, this dipole moment is called

polarization vector Nq P δ E

ind

0

fre

Property of the material: Dielectric susceptibility

Polarization charges induced on the surface:

For small displacements: P~E; P=

The field inside the dielectric is :

n

N

P

E

E

P n

reduced

e ind 0 free

0 0

ind free

11 ; ( )

E

K K

KK

K

Gauss’s Law in Dielectrics

0

( )i AEA

1

1i K

0

AKEA

0

freeQK E d A

Gauss’s Law inDielectrics

Forces Acting on Dielectrics

More charge here

We can either compute force directly(which is quite cumbersome), or use relationship between force and energy

F U

Considering parallel-plate capacitor 2

2

CVU

Force acting on the capacitor, is pointed inside,hence, E-field work done is positive and U - decreases

2

2xU V C

Fx x

x – insertion length

Two capacitors in parallel

0 01 2 w( ) w

KC C C L x x

d d

w – width of the plates

20w

( 1)2xV

F Kd

constant force