Electrostatics and Magnetostatics Nathaniel J C Libatique Ph

Electrostatics and Magnetostatics Nathaniel J. C. Libatique, Ph. D. nlibatique@gmail. com 3 December 2009

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Fields and Waves

Statics: very important Magnetic Storage: HDD Technology n Fields in transmission lines n MEMS actuators n E-Ink n Electrostatic separation n ESD n

HDDs Hitachi Introduces 1 -Terabyte Hard Drive Colossal storage reaches new milestone with a drive that holds 1000 gigabytes. Melissa J. Perenson, PC World Jan 5, 2007 1: 00 pm Hitachi Global Storage Technologies is first to the mat with an announcement of a 1 -terabyte hard disk drive. Industry analysts widely expected a 1 TB drive to ship sometime in 2007; Hitachi grabbed a head start on the competition by announcing its drive today, just before the largest U. S. consumer electronics show starts next week. http: //www. pcworld. com/article/128400/hitachi_introduces_1 terabyte_hard_drive. html

mcgonnigle. files. wordpress. com/2007/02/lightning. jpg ESD This failed IC was one of several rejected as low input resistance (leaky) at a particular input pin. Sectioning in Japan identified the partial short through the silicon from the top as shown by the small well on the track i. e. top of short circuit. This transistor was also confirmed failed by ESD. You can see where the discharge energy surge has buried through the weakest point(s) in the oxide layer through to the silicon. Bipolar devices are becoming very small and susceptible to ESD. http: //www. electrostatics. net/library/articles/ESD_damage. htm Photos from Rohm Electronics

Fields in Transmission Lines Two-wire Coaxial Microstrip Triplate

E-Ink http: //www. eink. com/technology/howitworks. html

MEMS http: //mems. sandia. gov/gallery/images/m 10. jpg

Capacitors and Inductors Capacitors store electric flux n Q = CV, i = Cd. V/dt n Charging up a capacitor: t = RC n Inductors store magnetic flux n Y = LI, v = Ldi/dt n Fluxing up an inductor: t = L/R n

Demonstrations Faraday’s Law n Lorentz Force n Conducting rod in a magnetic field n Deflecting electrons in a CRT via magnets n n Induced fields and currents in a 5 turn loop

How does one “see” an electric or magnetic field? Fields give rise to measurable forces n Static fields create “other” static fields n Dynamic fields give rise to “other” time varying fields n

Electrostatics: Coulomb’s Law F 1 Qe = - 1. 60219 x 10 -19 C eo = permittivitty of free space = 8. 854 x 10 -12 F/m 1/4 peo = 9 x 109 m/F R Q 1 F 1 = Qo Qo Q 1 4 p e 0 R 2 F 1 = Q 1 E 0 E-field source is Q 0 a 1

Electrostatic Field Sources Charge distributions give rise to E fields It takes work to “create” charge distributions, hence charge distributions store energy.

Ampere’s Force Law I 2 I 1 dl 1 a 12 R d. F 2 d. B 1 dl 2 d. F 2 = I 2 dl 2 d. F 1 = I 1 dl 1 (d. B) = Weber/m 2 k I 1 dl 1 a 12 R 2 k I 2 dl 2 a 21 R 2 k = mo/4 p; mo = magnetic permeability = 4 p x 10 -7 H/m

Biot-Savart Law Current distributions give rise to magnetic flux densities dl R I mo I dl a. R d. B = R 2 4 p A

Infinitely Long Straight Wire I mo I a B= 2 p r f B r ?

Infinite Plane Sheet of Current mo B= JS an 2 B JS ? ? B B

Infinite Plane Sheet of Current B B Superposition of many wires coming off the page…

Lorentz Force F = q (E + v B)

Slingshot • CRT • Ink Jet Printer • Mass Spectrometer • Electron Microscope • Particle Accelerators

Sample Feed A very low concentration of sample molecules is allowed to leak into the ionization chamber (which is under a very high vacuum) where they are bombarded by a high-energy electron beam. The molecules fragment and the positive ions produced are accelerated through a charged array into an analyzing tube. The path of the charged molecules is bent by an applied magnetic field. Ions having low mass (low momentum) will be deflected most by this field and will collide with the walls of the analyzer. Likewise, high momentum ions will not be deflected enough and will also collide with the analyzer wall. Ions having the proper mass-to-charge ratio, however, will follow the path of the analyzer, exit through the slit and collide with the Collector. This generates an electric current, which is then amplified and detected. By varying the strength of the magnetic field, the mass-tocharge ratio which is analyzed can be continuously varied. http: //www. chem. uic. edu/web 1/ocol/spec/MS 1. htm

http: //www. chem. ucalgary. ca/courses/351/Carey/Ch 13/ch 13 -ms. html

The mass spectrum of toluene (methyl benzene) is shown. The spectrum displays a strong molecular ion at m/e = 92, small m+1 and m+2 peaks, a base peak at m/e = 91 and an assortment of minor peaks m/e = 65 and below. The molecular ion, again, represents loss of an electron and the peaks above the molecular ion are due to isotopic abundance. The base peak in toluene is due to loss of a hydrogen atom to form the relatively stable benzyl cation. This is thought to undergo rearrangement to form the very stable tropylium cation, and this strong peak at m/e = 91 is a hallmark of compounds containing a benzyl unit. The minor peak at m/e = 65 represents loss of neutral acetylene from the tropylium ion and the minor peaks below this arise from more complex fragmentation. http: //www. chem. uic. edu/web 1/ocol/spec/MS 1. htm

Millikan Oil Drop e/m = charge to mass ratio n e = 1. 602 × 10 -19 Coulombs n http: //en. wikipedia. org/wiki/Oil-drop_experiment

Conduction • Electron Gas • Distribution of velocities: seen as temperature macroscopically • Electrons have mean free time between colllissions • vd = m E • J=s. E • Resistance vs. resistivity http: //hyperphysics. phy-astr. gsu. edu/Hbase/electric/ohmmic. html#c 1

The common U. S. wire gauges (called AWG gauges) refer to sizes of copper wire. The resistivity of copper at 20 C is about 1. 724 x 10 -8 W m AWG wire Diameter Resistance per size (solid) (inches) 1000 ft (ohms) 1000 m (ohms) 24 0. 0201 25. 67 84. 2 22 0. 0254 16. 14 52. 7 20 0. 0320 10. 15 33. 2 18 0. 0403 6. 385 20. 9 16 0. 0508 4. 016 13. 2 14 0. 0640 2. 525 8. 28 12 0. 0808 1. 588 5. 21 10 0. 1019 0. 999 3. 28 http: //hyperphysics. phy-astr. gsu. edu/hbase/Tables/wirega. html#c 1

Temperature Conductivity s coefficient x 107 /Wm per degree C Material Resistivity r (ohm m) Silver 1. 59 x 10^-8 . 0061 6. 29 Copper 1. 68 x 10^-8 . 0068 5. 95 Aluminum 2. 65 x 10^-8 . 00429 3. 77 Tungsten 5. 6 x 10^-8 . 0045 1. 79 Iron 9. 71 x 10^-8 . 00651 1. 03 Platinum 10. 6 x 10^-8 . 003927 0. 943 Manganin 48. 2 x 10^-8 . 000002 0. 207 Lead 22 x 10^-8 . . . 0. 45 Mercury 98 x 10^-8 . 0009 0. 10 Nichrome 100 x 10^-8 (Ni, Fe, Cr alloy) . 0004 0. 10 . . . 0. 20 Constantan 49 x 10^-8 http: //hyperphysics. phy-astr. gsu. edu/hbase/Tables/rstiv. html#c 1

Carbon* (graphite) 3 -60 x 10^-5 -. 0005. . . Germanium* 1 -500 x 10^-3 -. 05 . . . Silicon* 0. 1 -60 . . . -. 07 . . . Glass 1 -10000 x 10^9 . . . Quartz (fused) 7. 5 x 10^17 . . . 1 -100 x 10^13 Hard rubber

Hall Effect http: //hyperphysics. phy-astr. gsu. edu/hbase/magnetic/Hall. html#c 2

http: //content. honeywell. com/sensing/prodinfo/solidstate/technical/chapter 2. pdf http: //hyperphysics. phy-astr. gsu. edu/hbase/magnetic/hall. html#c 1 http: //hyperphysics. phy-astr. gsu. edu/hbase/electric/miccur. html#c 4 http: //www. allegromicro. com/en/Products/Design/hall-effect-sensor-ics/index. asp

Q = CV Y=LI d. Y/dt = L d. I/dt Electric field lines, magnetic flux lines Charging up a capacitor, differential equation solution, particular and homogeneous Fluxing up an inductor, differential equations Units and Dimensions