Electrical current effect range ?

[Externet]

A very long open canal dug on plain soil has contaminated water, or seawater if you prefer.

As very long means nothing; assume 10 Km.

 

Placing an electrode touching that water, with 120VAC 60Hz phase from mains; a sustantial current flows trough the water into ground.

(actually a 60W bulb in series is nearly at full brilliance !, say 80% (~0.4A) as conductivity is very high.)

 

Current path:

 

120VAC phase-------------------lightbulb---------------------------immersed in murky water-----------------------canalground.

 

[The bulb acts a current limiter]

 

How far reaching is the effect of the current ? Is there a way to calculate such distance? Obviously if done at a seashore, its effect will not reach the next beach.

 

Once I had the opportunity to satisfy my curiosity and dropped the 'grounding' electrode into the sea while arc welding on a 30m vessel next to a pier. Welding was difficult, current setting had to be raised in that condition, but was possible.

The current spread in seawater was near 100 Amperes. Zillions of marine microorganisms in the current path died instantly for sure. But how large could the affected area had been ?

[arc]

Externet, so your the guy behind that whole Philadelphia Experiment thing.

[studiot]

What you are asking is known as potential mapping.

There are various methods, using Coulombs law, conformal mapping with complex variables, Boussinesq method...

[Enthalpy]

conformal mapping with complex variables...

Conformal mapping works (sometimes) in 2D, that is when the electrodes run parallel to an other with a uniform section over an infinite extension. I dreamt about an extension to 3D, didn't find how to begin with that (quaternions? Their differential calculus remains to be invented), and gave up; I haven't heard about someone succeeding in this attempt.

 

More generally, zero method succeeds on real existing shapes. Algebraic solutions have been found for spheres, bifilar cables... But for a resistive canal in the ground, every attempt is futile, Boussinesq as much as the others. Either model the canal very grossly with a simple shape, or go to computers and finite elements.

 

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Phase connected to the canal ground: there is no limit to the extension of the current except Earth's size. Some (small) current will flow farther than the position of the return electrode, which is probably the next transformer making your 120Vac and its grounding electrode.

 

Though, we can try to estimate the distance where the injected current is less harmful. Imagine that the current spreads uniformly on a hemisphere (not realistic, but simple) up to the distance of the return electrode (and decreases faster beyond that distance). Let's say that 1mA in 1dm² is not immediately deadly for humans (but painful, and harmful over time for living organisms), then 100A must spread uniformly in 1000m² or 13m radius. Non uniform conductivity like the canal can make it worse. And anyway, little predictable conditions (like a conductive body and a dry soil) must let take huge margins.

 

Worse conditions exist when a medium or high voltage cable has fallen to Earth. People can get killed by walking on the ground, due to the potential gradient. First-aid workers learn to abandon victims of high-voltage until switched off and forbid access to avoid more victims. Bolt impacts also can kill through the potential gradient in the soil.

Edited June 28, 2013 by Enthalpy