How Do You Calculate the Electric Field from a Powerline?

[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, regardless of the change in voltage over time?

Thanks.

 

[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 capacitor 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.

 

[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...

 

[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.

 

[sardar]

Hello,

Thank you for your question. Yes, you are correct that the electric field around a current carrying wire will always be radial to the wire. This is because an electric field is created by the movement of charges, and in a current carrying wire, charges are constantly moving in the same direction along the wire.

To calculate the electric field from a powerline, you can use the formula E = V/d, where E is the electric field strength, V is the voltage, and d is the distance from the wire. The voltage you provided, V = |V| e^{i \omega t}, is the expression for a complex AC voltage, where |V| is the amplitude and \omega is the angular frequency. In this case, the electric field will also have a complex value, but the direction will still be radial to the wire.

It is important to note that the electric field strength will vary with distance from the wire, so it is important to consider the distance at which you are calculating the field. Additionally, the electric field will also vary with time, as the voltage on the wire changes. To get an accurate calculation, you may need to integrate the electric field over time.

I hope this helps answer your question. If you need further clarification or assistance with your calculations, please don't hesitate to reach out. Best of luck!

Sincerely,

Scientist