Electrostatics and Magnetostatics Nathaniel J. C. Libatique, Ph.D. 3 December 2009

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Fields and Waves

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

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, :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 1TB 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.

ESD Photos from Rohm Electronics 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. mcgonnigle.files.wordpress.com/2007/02/lightning.jpg

Fields in Transmission Lines Two-wire Coaxial Microstrip Triplate

E-Ink

MEMS

Capacitors and Inductors Capacitors store electric flux Capacitors store electric flux Q = CV, i = CdV/dt Q = CV, i = CdV/dt Charging up a capacitor:  = RC Charging up a capacitor:  = RC Inductors store magnetic flux Inductors store magnetic flux  = LI, v = Ldi/dt  = LI, v = Ldi/dt Fluxing up an inductor:  = L/R Fluxing up an inductor:  = L/R

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

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

Electrostatics: Coulomb’s Law QoQo Q1Q1 F1F1 F 1 = Q o Q 1 4   R 2 a1a1 F 1 = Q 1 E 0 R E-field source is Q 0 Q e = x C   = permittivitty of free space = x F/m 1/4  o = 9 x 10 9 m/F

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 I1I1 I2I2 dl 1 dl 2 R a 12 dF 2 dF 2 = I 2 dl 2  k I 1 dl 1  a 12 R2R2 dF 1 = I 1 dl 1  k I 2 dl 2  a 21 R2R2 dB 1 (dB) = Weber/m 2 k =  o /4  o = magnetic permeability = 4  x H/m

Biot-Savart Law Current distributions give rise to magnetic flux densities I dl A R dB =   I dl  a R R2R2

Infinitely Long Straight Wire I r ?B B =     r aa

Infinite Plane Sheet of Current JSJS ? B ? B B B =   JS  anJS  an

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

Lorentz Force F = q (E + v  B)

CRT Ink Jet Printer Mass Spectrometer Electron Microscope Particle Accelerators Slingshot

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-to- charge ratio which is analyzed can be continuously varied. Sample Feed

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. 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.

Millikan Oil Drop e/m = charge to mass ratio e/m = charge to mass ratio e = × Coulombs e = × Coulombs

Conduction Electron Gas Distribution of velocities: seen as temperature macroscopically Electrons have mean free time between colllissions v d =  E J =  E Resistance vs. resistivity

The common U.S. wire gauges (called AWG gauges) refer to sizes of copper wire. The resistivity of copper at 20 C is aboutresistivity x  m AWG wire size (solid) Diameter (inches) Resistance per 1000 ft (ohms) Resistance per 1000 m (ohms)

Material Resistivity  (ohm m) Temperature coefficient per degree C Conductivity  x 10 7 /  m Silver1.59x10^ Copper1.68x10^ Aluminum2.65x10^ Tungsten5.6x10^ Iron9.71x10^ Platinum10.6x10^ Manganin48.2x10^ Lead22x10^ Mercury98x10^ Nichrome (Ni,Fe,Cr alloy) 100x10^ Constantan49x10^

Carbon* (graphite) 3-60x10^ Germanium*1-500x10^ Silicon* Glass x10^9... Quartz (fused) 7.5x10^17... Hard rubber1-100x10^13

Hall Effect

Q = CV  = L I d  /dt = L dI/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