Charge distribution on a power line

[lagrangman]

I was trying to calculate the EMFs from power lines, just to see how they correspond to transmission line right of ways, and got a little stuck calculating the electrostatic E-field (-∇V) from power lines. I know it is dependent on the charge distribution on the power line, which is in turn dependent on the geometry.

So I have two questions:

How does one calculate the charge distribution or E-field from a single wire in free space at voltage V, with diameter d and length l?

How close is this approximation of self-capacitance to real capacitance encountered in power lines?

Thanks a lot.

 

[hutchphd]

I was trying to calculate the EMFs from power lines, just to see how they correspond to transmission line right of ways, and got a little stuck calculating the electrostatic E-field (-∇V) from power lines. I know it is dependent on the charge distribution on the power line, which is in turn dependent on the geometry.

So I have two questions:

How does one calculate the charge distribution or E-field from a single wire in free space at voltage V, with diameter d and length l?

How close is this approximation of self-capacitance to real capacitance encountered in power lines?

Thanks a lot.

I assume you want the potentials "far" from the wires..like near the ground. The details of the distribution won't really matter.
Is this DC??

 

[lagrangman]

Yes, I want the E-field near ground (as in the laymans ground). I was thinking for AC, but I figured it is low enough frequency that the max radial E-field would be the same as DC.

 

[hutchphd]

The Earth is flat conductor at zero potential (for low frequency). So one uses the "method of images" and puts an imaginary opposite line of charge underground. The field is the sum of the two.

 

[lagrangman]

So if a power line is at 12 kV rms (amplitude of 17 kV) single line Earth return, with a pole height of 20 meters, would the max radial E-field be approximately 850 V/m?

Also, how would I go about calculating the three phase E-field at near layman's ground?

Thanks a lot for your help so far.

 

[hutchphd]

That seems a reasonable result.
You should also be aware that the Earth itself has a natural DC field of several hundred V/M from surface to ionosphere!
Three phase power gives a very very much reduced extended field profile...it is one reason it is so popular. Read up on it a little and I will try to answer questions (and there are other people here who really know this stuff !).

 

[anorlunda]

Don't forget with AC, that the field goes through zero and reverses direction 120 times per second.

At ground level, you shouldn't see much difference between single phase and three phase, so I would ignore it.

Here is a website dedicated to just the kind of info you're asking about.

http://www.emfs.info/sources/overhead/
Here is one of the graphics from that site.

 

[lagrangman]

Thanks a lot for the help. I did see that website, but it did not seem to specify whether the E-fields were radial (-∇V) or axial ($-\frac{1}{c}\frac{dA}{dt}$) or how they were calculated. I will definitely read up on it more.