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

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=0 outside field did not change Potential difference (which is the integral of field) is, however, smaller.

Properties of Dielectrics Redistribution of charge – called polarization We assume that the induced charge is directly proportional to the E-field in the material dielectric constant of a material when Q is kept constant In dielectrics, induced charges do not exactly compensate charges on the capacitance plates

Induced charge density Permittivity of the dielectric material 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) Electric field density in the dielectric Example: A capacitor with and without dielectric Area A=2000 cm 2 d=1 cm; V 0 = 3kV; After dielectric is inserted, voltage V=1kV Find; a) original C 0 ; b) Q 0 ; 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.

C/A=7.3  F/m 2 Time to charge outer surface of a parallel plate capacitor to some voltage with respect to spacecraft frame is: 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/m 2, 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 3.5  F/m 2 and the charging time would have been 132 s - no discharge would have occurred.

Molecular Model of Induced Charge Electronic polarization of nonpolar molecules

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

Gauss’s Law in Dielectrics

Forces Acting on Dielectrics More charge here We can either compute force directly (which is quite cumbersome), or use relationship between force and energy Considering parallel-plate capacitor Force acting on the capacitor, is pointed inside, hence, E-field work done is positive and U - decreases x – insertion length Two capacitors in parallel w – width of the plates constant force