MadSci Network: Physics

Re: What is the formula that determins how far electricity can jump based on

Date: Mon Feb 6 14:12:02 2006
Posted By: Aaron J. Redd, Post-doc/Fellow, Plasma Physics and Controlled Nuclear Fusion, University of Washington
Area of science: Physics
ID: 1138815301.Ph
Message:

Hello, Chris.

The short answer:  Suppose you have a pair of conductors (bare copper
cables, for example), one grounded and one electrically charged to some
voltage.  The air around that charged conductor can break down (or "spark"
or "spark over") and conduct electricity over to the grounded conductor
when the voltage between them is too high. "Too high" is related to the
distance between them, and is 30,000 Volts/centimeter in dry sea-level air.
 So, for two bare cables separated by 15 centimeters, you can expect a
spark'n'arc to form between them if there is a voltage of 450,000 Volts.

The long answer:  Obtain a physics textbook, and read about electric
charge, electric fields, electric potential/voltage, and capacitance and
dielectrics.  (These topics will certainly be covered in any calculus-based
college physics textbook, but might be well-explained a high-school text --
you might need to ask your physics teacher for the name of a good book.) 
The short answer I gave you above leaves out a lot of details, and details
certainly matter.  The breakdown is actually related to the strength of the
local electric field, which can be strongly affected by the geometry (sharp
edges and corners make sparks happen easier).  You can also put materials
in between the conductors that increase the "dielectric strength", and make
it harder for sparks to form: pyrex glass, teflon or even paper, for instance.

A spectacular example of sparks jumping across a gap and forming an arc is
the "Jacob's Ladder", which usually turns up in low-budget science fiction
movies:  If you've ever seen a device with two near-vertical wires, with a
spark that jumps between them and then moves upward, and a new spark
forming down below as the old one reaches the ends of the wires, that's a
Jacob's Ladder.

I should also point out that, while watching sparks jump across gaps might
be fun, you need to be very careful when you're working with electricity,
and especially with high voltages.  30000 V/cm is a guide, but you should
never rely on that to keep you safe -- to put it another way, it'd be
pretty stupid to stand just a few feet away from a charged 10kV capacitor
bank on a humid day, and point at it: if you're lucky you'll just lose a
finger.  Play it safe, be very very careful, and ALWAYS have someone
working with you or watching you, preferably someone who knows CPR.

Long answer to a short question.  I hope this helps.  Good Luck!

Aaron




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