# Electric field of powerline

1. Jun 2, 2008

### Nick89

Hi,

How can I calculate the electric field from a powerline?

I need to calculate the electric field around a current carrying wire with an AC voltage. I don't know the current, I only know the voltage that is on the wire. For example, the voltage could be $$V = |V| e^{i \omega t}$$ where $\omega$ is ofcourse the angular frequency of the AC voltage.

Am I right that the direction will always be radial to the wire, irregardless of the change in voltage over time?

Thanks.

2. Jun 2, 2008

### mgb_phys

In simple terms the field is just radial form the wire.
If you need a more realistic answer you have to take into account the ground underneath the wire. The field will look like a capcitor between the ire and the ground below and a simple field extending into space everywhere else.

Capcitance losses to the ground are the major source of loss in high V transmission lines and is one of the reason for using high towers rather than burying cables.

3. Jun 2, 2008

### Nick89

I know the ground will disturb the field rather much, however I was trying to calculate the field in empty space first, and then try to compare it with measurements from real powerlines and explain the differences.

My question is still open, I still didn't figure out how to actually calculate the electric field on a wire if the only thing I know is the voltage. If I knew some sort of charge distribution it would be trivial but afaik this can't be derived from voltage only, right?

Come to think of it, I don't even know how to calculate it if the voltage is just constant...

4. Apr 19, 2011

### Don Kelly

Apologies but I have just seen this thread, being a newcomer to the forum

mgb_phys is in error-or, at least oversimplifying. the capacitance of a high voltage power line is definitely not the major source of losses. Resistance is. A line may be inductive or capacitive depending on its length and loading. Lines are high to reduce ground level fields and to give greater clearance at higher voltages.

As to calculation of the electric fields -given the voltages, positions and radii of the conductors it is a simple process to determine the charges and then the field. The method of images is used and while this is not exact as the ground is not a perfect conducting plane but the errors are negligible.

Matrix P has elements (see any power system (engineering) text.
Pij= (1/2piE0)*ln dij/Hij where dij is the distance between conductors i and j and Hij is the distance between conductor i and the image of conductor j
Q =[P^-1]V
Now given Q the field at any point can be found from the sum of fields due to individual line and image charges.