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Prof. D. Wilton ECE Dept.
Notes 19
ECE 2317 ECE 2317 Applied Electricity and MagnetismApplied Electricity and Magnetism
Notes prepared by the EM group,
University of Houston.
Dielectric BreakdownDielectric Breakdown1 Arcing (spark)
Ec = “critical electric field” (air ionizes)
Air
Oil
Glass
6
6
6
3 10 V/m
15 10 V/m
30 10 V/m
c
c
c
E
E
E
+ -
Ex Ex = Ec x
Dielectric Breakdown (cont.)Dielectric Breakdown (cont.)2 Corona Discharge (local breakdown)
+ -
E > Ec
Power line
Lines are sometimes grouped to reduce losses and corona effect.
ExampleExample
coaxial cable
a
b
r
6
2.0
15 10 [V/m]
0.25 cm
0.5 mm
r
cE
b
a
Find: Vmax (assume a safety factor SF = 2 )
max
0
maxmax
0
2
:
2 SF
r
c
r
E
a
EE
a
Set
lmax
-lmax
+
++
+
++
-
---
- -
Example (cont.)Example (cont.)Thus max
02SF
cr
Ea
max
0
max
2 SF
SF
lnSF
c
r
B b
AB
A a
bc
a
b
c
a
E aE
V V E dr E d
E ad
Ea
Hence
or max lnSF
cE bV a
a
ExampleExample
Hence:
max
63
ln
15 100.5 10 ln 5
2
cE bV a
SF a
max 6035.4 V
6.04 kV
V
Van de Graaff GeneratorVan de Graaff Generator
Electric field is high near sharp points: charges are free to jump on/off
Faraday cage effect: no matter how much charge is placed on the dome, it goes to the outside and there is little field on the inside
Principles:
Dr. Robert J. Van de Graaff (1901-1967) was a professor at Princeton university and a Research Associate at MIT. The Van de Graaff generator was invented in 1929 and originally used as a research tool in early atom-smashing and high energy X-ray experiments.
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
This picture shows Dr. Van de Graaff with his first generator (80 [kV]).
The world’s largest air-insulated Van de Graaff generator, designed and built by Van de Graaff during 1931-1933. The spheres are 15 feet in diameter and 43 feet off the ground. It can produce 7 [MV].
Inside each dome there was a laboratory.
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
In the early 1950's, the giant Van de Graaff generator was donated to the Boston Museum of Science.
For years, it was enclosed in a small steel structure on the Museum's property, where it was occasionally demonstrated.
Finally, in 1980, the Thomson Theatre of Electricity was completed inside the museum. The generator is demonstrated at least twice daily, to teach public and school audiences about electricity and lightning.
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
A modern Van de Graaff generator integrated with a particle accelerator. The generator produces the high voltages (in the megavolt range) that accelerates particles.
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
For more information:
http://en.wikipedia.org/wiki/Van_de_Graaff_generator
Van de Graaff Generator (cont.)Van de Graaff Generator (cont.)
Example (demo)Example (demo)
Van de Graaf: Find maximum V0
a
r cr aE E
max2
0
2max 0
2max 0
00 0
0
4
4
4
4 4
c
c
c
c
QE
a
Q a E
Q a EV
a a
V a E
Qmax
+
+
+++
+
+
+
Example (cont.)Example (cont.)
Assume 6
0.1 m
3 10 V/mc
a
E
Maximum spark length:
V0
h 0
0.1 mc cV a E E h
h a
0 300,000 VV
0.1 m ( 3.9 inches)h h Approximate the spheres as flat conductors.
6max 3.33 10 3.33 CQ
LightningLightning
Lightning (cont.)Lightning (cont.)
_ _ _ _ _ _ _ _ _
+ + ++ + + + + +
Earth
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Most lightning comes from negative charges at the base of a thundercloud. Only about 5% comes from the positive charges at the top.
Lightning (cont.)Lightning (cont.)
_ _ _ _ _ _ _ _ _
+ + ++ + + + + +
Earth
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
The base of the thundercloud is typically at an altitude of about 1,500 [m]. The top of the thundercloud may be at about 10,000 [m].
The voltage drop between the cloud base and ground is typically 150 [MV].
Lightning (cont.)Lightning (cont.)
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
Earth
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
A “stepped leader” begins descending from the cloud. It is a group of electrons that zigzags toward the earth. The charge is typically about -5 [C].
The stepped leader starts descending down at a speed of about 17% the speed of light. It travels about 50 [m] in about 1 [s] pauses for about 50 [s], then continues, pausing every 50 [m] or so. The average speed is about 150 [km/s].
The stepped leader does not know where it will strike until it is about 20-50 [m] from the earth (40 [m] is typical).
Lightning (cont.)Lightning (cont.)
Earth
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
The stepped leader may branch as it descends (this is responsible for the forked appearance of some lighting).
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
Lightning (cont.)Lightning (cont.)
Earth
As the stepped leader approaches the earth, positive “streamers’ rise up from the earth to meet it.
The streamers are more likely to come from conducting objects with sharp points.
Streamers may be up to about 50 [m] in length
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
++
++
++
--
Lightning (cont.)Lightning (cont.)
Earth
At a height of about 40 [m], a streamer meets with the stepped leader, and a conducting channel is formed to earth.
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Lightning (cont.)Lightning (cont.)
Earth
A powerful surge of current (“return stroke”) flows upward from the ground to the cloud. This is what is visible as the lightning bolt.
The current surge travels upward at about 25% the speed of light. The charge in the branches is drained as the surge passes by.
The peak current is typically 10 to 20 [kA]. The return stroke typically lasts about 100 [s].
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
---
current surge
Lightning (cont.)Lightning (cont.)
main channel
branches
Lightning (cont.)Lightning (cont.)
Earth
The current stops for about 50 [ms].
A new leader, called the “dart leader” descends from the cloud along the previous path.
The dart leader travels at about 2000 [km/s] (about 10 times faster than the stepped leader) without pausing. It carries about -1 [C].
Another return stroke occurs when the dart leader reaches the ground.
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Lightning (cont.)Lightning (cont.)
Earth
The dart-leader / return-stroke combination repeats typically 3 or 4 times.
The entire lighting flash lasts typically 0.2 [s] (sometimes as long a 1 [s] or more).
The total charge deposited on the ground is about -25 [C].
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Lightning (cont.)Lightning (cont.)
Earth
+ + + + + + + + + + +
Lightning (cont.)Lightning (cont.)
_ _ _ _ _ _
+ + + + + +
– – – – – – – – – – – –
Less common (about 5% of the total) but far more dangerous, are “positive” lightning strikes occurring between the positively charged tops of clouds and the ground, often several miles away.
These so-called “bolts out of the blue” typically average 10 times the charge and voltage differences of a “negative” strike.
Lightning RodLightning Rod
Earth
A lighting rod is a rod of metal that is well grounded, and ideally sharp at the end.
It launches a good streamer (better than the surrounding points on the building) because of the high electric field near the tip.
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
high E
Lightning SafetyLightning Safety
1. The best protection is to be inside of a closed metal structure such as an automobile (Faraday cage effect).
2. If outside:
• Make sure you are not the tallest object around.
• Do not stand near the tallest object around.
• Do not carry metal poles or metal objects (golf clubs,etc.).
3. If you must be in an open field, crouch down, put your feet together, face away from any taller objects, and cover your ears.
Lightning Safety (cont.)Lightning Safety (cont.)
Earth
The ground current near the strike may be very large.
This causes a large electric field along the surface of the earth.
It is possible to be electrocuted without being hit by the lightning.
Best to keep your feet together!
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
E
+-
1
J E
E J
Lightning Safety (cont.)Lightning Safety (cont.)
Earth
sample calculation
_ _ _ _ _ _ _ _ _
+ + + + + + + + +
E
+-
I = 20 [kA]r = 10 [m] = 0.1 [S/m]
20.5 4
1
r
r r
IJ
r
E J
r
Er = 318 [V/m]
(current spreading over a hemisphere)
(point form of Ohm’s law)
I
Also, it is best to keep your feet along a line that is perpendicular to the direction pointing to the tallest object nearby. lightning contact point (e.g., a tree)
your feet
E
Lightning Safety (cont.)Lightning Safety (cont.)
equipotential contour
Other Lightning-Like Atmospheric Other Lightning-Like Atmospheric DischargesDischarges
