Download PHYS_3342_100411

The graded exams are being returned today. You will have until the next class on
Thursday, Oct 6 to rework the problems (including the multiple choice questions) you
got wrong and receive 50% added credit. You are honor bound to work on these
alone; this is an exam. I will be going over the answers in class next Tuesday. This
will also be your only opportunity to ask for corrections/clarifications on any grading
mistakes.
Capacitor 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.
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.
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 parallelplate capacitors - top plate
consists of electrons buried
in top few microns of Teflon.
1 22 1

C i1 c i
C/A=7.310-9 F/m2
 of a parallel plate capacitor to some voltage with
Time to charge outer surface
respect to spacecraft frame is:
t
CV
i(1   )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 3.510-7 F/m2 and the
charging time would have been 132 s - no discharge would have occurred.
Electric Current
Charges in Motion – Electric Current
Electric Current – a method to deliver energy
Very convenient way to transport energy
no moving parts (only microscopic charges)
Electric currents is in the midst of electronic circuits
and living organisms alike
Motion of charges in electric fields
Force on a particle : F  qE
Accelerati on : a  F / m
d 2r
Equation of motion : m 2  qE(r, t )
dt
When E is time - independen t, the total energy is conserved :
mv2
 q (r )  const
2
Motion in a uniform electric field
For x - components :
a  qE / m
v(t )  v0  at
at 2
x(t )  x0  v0t 
2
Other components of v do not change
Deflection by a uniform electric field
x  vi t
qE 2
y
t
2m
y   x 2 : Parabolic trajector y
v fx  vi
qE l
v fy  
m vi
Application: Cathode Ray Tube
Electric Current in Conductors
In electrostatic situations – no E-field inside
There is no net current. But charges (electrons)
still move chaotically, they are not on rest.
On the other side, electrons do not move with
constant acceleration.
Electrons undergo collisions with ions. After
each collision, the speed of electron changes
randomly.
The net effect of E-field – there is slow net
motion, superimposed on the random motion
Vchaotic ~ 106 m / s
Vdrift ~ 104 m / s
Direction of the Electric Current
is associated with the rate of flow of charge
ΔQ
dQ

Δt
dt
1 Coulomb
Unit : 1 Ampere 
1 second
Current density is the current per unit area :
through surface A : I 
I
J
A
Current in a flash light ~ 0.5 A
In a household A/C unit ~ 10-20 A
TV, radio circuits ~ 1mA
Computer boards ~ 1nA to 1pA
Current, Drift Velocity, Current Density
Q  qnAvd t

J

I Q

 qn v d [ A / m 2 ]
A At
Concentration of mobile charge
carriers per unit volume: n
Average speed in the direction
of current (drift speed): vd
For a variety of charge carriers:


J   | qi | ni v d
i
Current density J, is a vector
while total current I is not


I   J d S
Example: An 18-gauge copper wire has nominal
diameter of 1.02 mm and carries a constant current
of 1.67 A to 200W lamp. The density of free electrons
is 8.5*1026 el/m3. Find current density and drift velocity
J
I
4I

A d2
J  nevd ;
2  106 A / m2
vd  1.5  104
m/ s
Why, then, as we turn on the switch, light comes
immediately from the bulb?
E-field acts on all electrons at once (E-field
propagates at ~2 108 m/s in copper)
Electric current in solution of NaCl is due to
both positive Na+ and negative Cl- charges flow
Ohm’s Law
Current density J and electric field E are established inside a conductor when a
potential difference is applied –
Not electrostatics – field exists inside and charges move!
In many materials (especially metals)
over a range of conditions:
J = σE or J = E/r
with E-independent conductivity σ=1/r
This is Ohm’s law
(empirical and restricted)
Conductors, Insulators and
Semiconductors
Resistance of a straight wire
V
I  J  A E  A A
L
1
I  V (V  Vb  Va  b   a )
R
L
Resistance R 
A
1 Volt
Unit: 1 Ohm () 
1 Ampere
1
Resistivity
r

Unit:
V=IR
1 m
L
Rr
A
Water Flow Analogy
Interpreting Resistance
I-V curves
ohmic
nonohmic
(linear)
(non-linear)
Resistivity and Temperature
r(T) = r0[1+a(T-T0)]
Electrical Shock
“It’s not the voltage but the current.”
The current is what actually causes a shock - human body has resistance of ~500,000 
with dry skin - ~100  wet! Requires conducting path.
Can cause: (1) burning of tissue by heating, (2) muscle contractions, (3) disruption of
cardiac rhythms.
Current (A)
Effect
0.001
Can be felt
0.005
Is painful
0.010
Causes spasms
0.015
Causes loss of muscle control
0.070
Goes through the heart - fatal after more than
1 second
Charging on Astronaut Space Suit in Auroral Zone: Potentially hazardous situation
– EVA Suit Specified to –40 V
• anodized coating arcing occurred
at –68V in MSFC test
– Possible Sneak-Circuit
• 1 mA safety threshold
Metal waist and neck rings and other metal
portions of the suit make contact with the
sweat soaked ventilation garment providing
possible conducting path for discharge through
astronaut’s thoracic cavity.
Safety
 Surface of spacesuit could charge to high
voltage leading to subsequent discharge.
Display
and
Control
Module
(DCM)
Tether
Discharge to the station through safety tether:
• Tether is a metallic cable - connected to
astronaut via non-conducting (nylon)
housing.
• Station maintained at plasma potential arc path closed when tether gets
wrapped around astronaut.
Mini Work Station
(MWS)
Body Restraint
Tether (BRT)