Fall 2004

Dielectric breakdown

ECE 2317: ECE 2317: Applied Electricity and MagnetismApplied Electricity and Magnetism

Prof. Jeffery T. WilliamsDept. of Electrical & Computer Engineering

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 BreakdownDielectric Breakdown2 Corona Discharge

+ -

E > Ec

Power line

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

max

0

ˆ2

2

r

cr

E

a

Ea

ρ

Set

lmax

-lmax

ExampleExampleThus max

02 r ca E

m

max

0

max

ax

ˆ ˆ

l

ln

2

n

cr

B b

AB

A a

b

c

a

b

c

c

a

aE

V V d E d

bV E

E d

E

a

a

a

a

E ρ ρ

E

Hence

or

ExampleExampleWith safety factor:

max

max

6 3

6035

1ln

115 10 0.5 1

.4

0 ln 52

SF

SFc

bV E a

SF a

V 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

Example (classroom demo)Example (classroom 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

0.1 m

3 10 V/m

300,000 V

C

a

E

V

Maximum spark length:

V0

h

0

50

6

3 10 V

3 10 V/m

0.1 m

( 3.9 inches)

c

c

V E h

Vh

E

h

h

LightningLightning

LightningLightning

LightningLightning

_ _ _ _ _ _ _ _ _

+ + ++ + + + + +

Earth

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Most lightning comes from negative charges at the base of the thundercloud. About 10% comes from clouds with positive charges at the base.

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].

LightningLightning

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 travels at an average speed of about 150 [km/s] (0.05% the speed of light). It travels about 50 [m] in about 1 [us] (about 10% the speed of light), pauses for about 50 [us], then continues.

The stepped leader does not know where it will strike until it is about 20-50 [m] form the earth (40 [m] is typical).

_ _ _ _ _ _ _ _ _

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LightningLightning

Earth

The stepped leader may branch as it descends (this is responsible for the forked appearance of some lighting).

_ _ _ _ _ _ _ _ _

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LightningLightning

Earth

As the stepped leader descends, positively charged “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 +

+

++

++

--

_ _ _ _ _ _ _ _ _

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++

++

+

LightningLightning

Earth

At a height of about 40 [m], a streamer meets with the stepped leader, and a conducting channel is formed to earth.

_ _ _ _ _ _ _ _ _

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++

++

+

LightningLightning

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 average current is typically 10 to 100 [kA]. The return stroke lasts about 0.1 [ms] to 1 [ms].

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---

current surge

_ _ _ _ _ _ _ _ _

+ + ++ + + + + +

LightningLightning

main channel

branches

LightningLightning

Earth

The current stops after 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.

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LightningLightning

Earth

The dart-leader / return-stroke combination repeats typically 3 or 4 times.

The entire lighting flask lasts typically 0.2 [s] (sometimes as long a 1 [s] or more).

The total charge deposited on the ground is about -20 [C].

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_ _ _ _ _ _ _ _ _

+ + ++ + + + + +

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.

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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.

• Do not carry metal poles or metal objects (golf clubs,etc.).

3. If you must be in an open field, lie down in the lowest lying area, and cover your ears.

Lightning SafetyLightning Safety

Earth

The ground current near the strike may be very large.

This causes an 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

_ _ _ _ _ _ _ _ _

+ + ++ + + + + +