Electrostatics and
Magnetostatics
Nathaniel J. C. Libatique, Ph.D.
nlibatique@gmail.com
3 December 2009
f c
Fields and Waves
Statics: very important
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Magnetic Storage: HDD Technology
Fields in transmission lines
MEMS actuators
E-Ink
Electrostatic separation
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, 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 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.
http://www.pcworld.com/article/128400/hitachi_introduces_1terabyte_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/m10.jpg
Capacitors and Inductors
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Capacitors store electric flux
Q = CV, i = CdV/dt
Charging up a capacitor: t = RC
Inductors store magnetic flux
Y = LI, v = Ldi/dt
Fluxing up an inductor: t = L/R
Demonstrations
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Faraday’s Law
Lorentz Force
Conducting rod in a magnetic field
 Deflecting electrons in a CRT via magnets
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Induced fields and currents in a 5 turn loop
How does one “see”
an electric or magnetic field?
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Fields give rise to measurable forces
Static fields create “other” static fields
Dynamic fields give rise to “other” time varying
fields
Electrostatics: Coulomb’s Law
F1
Qe = - 1.60219 x 10-19 C
eo = permittivitty of free space
= 8.854 x 10-12 F/m
1/4peo = 9 x 109 m/F
R
Q1
F1 =
Qo
Qo Q1
4 p e0 R2
F1 = Q1 E0
E-field source is Q0
a1
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
I2
I1
a12
dl1
R
dF2
dB1
dl2
dF2 = I2 dl2 
dF1 = I1 dl1 
(dB) = Weber/m2
k I1 dl1  a12
R2
k I2 dl2  a21
R2
k = mo/4p; mo = magnetic permeability
= 4p x 10-7 H/m
Biot-Savart Law
Current distributions give rise to magnetic flux densities
dl
R
I
mo I dl  aR
dB =
R2
4p
A
Infinitely Long Straight Wire
I
mo I a
B=
2p 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/web1/ocol/spec/MS1.htm
http://www.chem.ucalgary.ca/courses/351/Carey/Ch13/ch13-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/web1/ocol/spec/MS1.htm
Millikan Oil Drop
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e/m = charge to mass ratio
e = 1.602 × 10-19 Coulombs
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=sE
• Resistance vs. resistivity
http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/ohmmic.html#c1
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 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#c1
Temperature
Conductivity s
coefficient
x 107 /Wm
per degree C
Material
Resistivity r
(ohm m)
Silver
1.59 x10^-8
.0061
6.29
Copper
1.68 x10^-8
.0068
5.95
Aluminum
2.65 x10^-8
.00429
3.77
Tungsten
5.6
x10^-8
.0045
1.79
Iron
9.71 x10^-8
.00651
1.03
Platinum
10.6 x10^-8
.003927
0.943
Manganin
48.2 x10^-8
.000002
0.207
Lead
22
x10^-8
...
0.45
Mercury
98
x10^-8
.0009
0.10
Nichrome
100 x10^-8
(Ni,Fe,Cr alloy)
.0004
0.10
...
0.20
Constantan
49
x10^-8
http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/rstiv.html#c1
Carbon*
(graphite)
3-60
x10^-5 -.0005 ...
Germanium*
1-500
x10^-3
-.05
...
Silicon*
0.1-60
...
-.07
...
Glass
1-10000
x10^9
...
...
Quartz
(fused)
7.5
x10^17
...
...
1-100
x10^13
Hard rubber
Hall Effect
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Hall.html#c2
http://content.honeywell.com/sensing/prodinfo/solidstate/technical/chapter2.pdf
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/hall.html#c1
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html#c4
http://www.allegromicro.com/en/Products/Design/hall-effect-sensor-ics/index.asp
Q = CV
Y=LI
dY/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