# How does the strength of an electrical field vary with the distance from it?

#### Theophila

Joined Nov 20, 2014
15
I'm a home buyer, reluctant to buy too near those high tension towers. They usually give me a headache when I drive under them.

I know the strength of a small charge's field varies 1/r x r, where r is the distance from it. I read that formula doesn't hold for fields generated by a large charge.

I would appreciate a referenced answer Thank you!

#### MikeML

Joined Oct 2, 2009
5,444
Let me guess, you worry about 60Hz power lines a 1/4 of a mi away, but you walk around all day with a rf emitting device stuck in your ear.

#### Theophila

Joined Nov 20, 2014
15
To quote Moe Howard, "Yer wrong, Quiz Kid."

I even resisted getting a wireless mouse until only they were available.

But I posted here in order to get an intelligent answer, not sarcasm. If you have nothing better to do, just ignore this thread, OK? Thanks, and have a nice day.

#### MikeML

Joined Oct 2, 2009
5,444

#### BR-549

Joined Sep 22, 2013
4,928
In a strict sense.....the inverse square law only works with point sources. It's the geometric shape of the flux field from a single point that is the cause of the inverse square law. A point source of ANY amount of charge will obey this law.

This is not stressed enough in physics. It is the PHYSICAL structure of the flux, that is the cause of the inverse square law.

Many, many studies have been done by people who hate power lines and nothing concrete has been found.

The human body can pass low frequency electric fields very easily. I would be more worried about a cell phone antenna 2" from my skull.

#### Theophila

Joined Nov 20, 2014
15
My sarcasm was intended to point out the reality of the inverse square law...
You mean the inverse square law to which I referred in my question? Your answer doesn't tell me how the strength of the field varies if the source is not a point.

#### Theophila

Joined Nov 20, 2014
15
In a strict sense.....the inverse square law only works with point sources. It's the geometric shape of the flux field from a single point that is the cause of the inverse square law. A point source of ANY amount of charge will obey this law.

This is not stressed enough in physics. It is the PHYSICAL structure of the flux, that is the cause of the inverse square law.

Many, many studies have been done by people who hate power lines and nothing concrete has been found.

The human body can pass low frequency electric fields very easily. I would be more worried about a cell phone antenna 2" from my skull.
If you can post a link to one such study, I would like to see it. Thanks")

#### studiot

Joined Nov 9, 2007
4,998
Hello and welcome, Theophila, and how's your maths?

The strength of the electric field can be measured in a number of ways and is given by some high powered equations, known as Maxwell's equations.

There are four of these and the second one refers to the electric field exclusively.
The solution to this equation gives the spatial distribution of the field due to any arrangement of charges, but analytical (formulae) solutions are not easy to come by and more complicated patterns are usually worked out by numerical methods with a computer.

Edit I meant to say that BR549 was right for once in that the inverse square law is the solution to this equation for a single point charge.

We can however make approximations to many simple arrangements such as the field set up by one or two wires, a plate, a cylinder and so on.

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#### BR-549

Joined Sep 22, 2013
4,928

#### alfacliff

Joined Dec 13, 2013
2,458
when googling "power line radiation" or any other highly argued subject, beware of the well intentioned people who really dont know a thing about the subject, but are "experts" on it. basicly university studies might be trusted more than a "wild eyed pistol waver".

#### BR-549

Joined Sep 22, 2013
4,928
I lost my hair many years ago. I am sure that I reflect most all frequencies.
Most of the sun's spectrum that reaches me, my hard headed skull will block.

Cell phone frequencies just love bone and water.
They go right to the brain stem and react with the quantum effect, causing all loss of, and understanding of, common sense.

No experimentation is required to observe this.

#### nsaspook

Joined Aug 27, 2009
10,919
Cell phone frequencies just love bone and water.
They go right to the brain stem and react with the quantum effect, causing all loss of, and understanding of, common sense.

No experimentation is required to observe this.
Use a cell phone much?

#### Theophila

Joined Nov 20, 2014
15
Hello and welcome, Theophila, and how's your maths?

The strength of the electric field can be measured in a number of ways and is given by some high powered equations, known as Maxwell's equations.

There are four of these and the second one refers to the electric field exclusively.
The solution to this equation gives the spatial distribution of the field due to any arrangement of charges, but analytical (formulae) solutions are not easy to come by and more complicated patterns are usually worked out by numerical methods with a computer.

Edit I meant to say that BR549 was right for once in that the inverse square law is the solution to this equation for a single point charge.

We can however make approximations to many simple arrangements such as the field set up by one or two wires, a plate, a cylinder and so on.
Thanks. I will Google Maxwell's second equation and see if my maths are up to it.

#### Theophila

Joined Nov 20, 2014
15
Thanks. I will Google Maxwell's second equation and see if my maths are up to it.

#### joeyd999

Joined Jun 6, 2011
4,714
I'm a home buyer, reluctant to buy too near those high tension towers. They usually give me a headache when I drive under them.
This would make you an overhead power line detector. If I thought I "usually" got headaches from driving under power lines, I'd want to prove it.

I'd have a friend blindfold (and earplug) me and drive me around unfamiliar parts of town, both under high-tension lines, and far away from them. I'd track the ride vs. gps, and note my "headache condition" vs. time. At the end of the trip, I'd have a third party match headaches vs. position, and position vs. power lines. If I indeed had a propensity to headaches near powerlines, this should result in a strong correlation. If not, it would show that I'm full of c***, probably more often than I am aware.

I know the strength of a small charge's field varies 1/r x r, where r is the distance from it. I read that formula doesn't hold for fields generated by a large charge.
For an infinitely long and straight power line (this is a reasonable assumption for small r), the answer is 1/r.

#### joeyd999

Joined Jun 6, 2011
4,714
For an infinitely long and straight power line (this is a reasonable assumption for small r), the answer is 1/r.
See, I am full of c***. This'd be for a single conductor.

High tension lines come in sets of three, one for each phase.

The E fields should cancel to zero a short distance away, I think.

#### MikeML

Joined Oct 2, 2009
5,444
This would make you an overhead power line detector...
You are way too polite...

#### studiot

Joined Nov 9, 2007
4,998
Thanks. I will Google Maxwell's second equation and see if my maths are up to it.
The how's your maths was an offer to help further by the way.

You asked specifically about electric fields, but usually (and always when there is moving charge or electric current involved) there are both electric and magnetic fields involved.

These have different effects.

The magnetic fields cause heating in susceptible materials, depending upon frequency, field strength and the material concerned.
So for instance the magnetic component of microwaves heats water molecules.

Electric fields do not cause heating.

One effect that has been noted is the beneficial increase in wound healing rate, pioneered by a unversity hospital in New York.
Apparantly apply the right electric field across the wound speeds up the healing, for unknown reasons.

Back to Maxwell's equations, the four equations completely describe electric and magnetic effects between them.

Maxwell II often reduces to Gauss' Law or Laplaces Equation and in many cases can be reduced still further.