Size of an object not connected to safety physical earth, to be effective earth?!

[Al (astral highway)]

This is a meandering lead-in but I hope you’ll stay with me. I am in hosp stil and away from the practical world of making and observing, but my mind is entertaining me.

I noticed,before my recent construction break, that even when I was standing a couple of metres away from an antinode radiating plasma (HF- and a stub at the end of a resonant inductor, not an antenna designed to transmit intelligence, if you’re interested!) that I became RF ‘hot’. By this I mean that when I touched a metal object nearby, I received a tiny RF burn at the point of contact. We’re talking approx just 20W RF out)

This led me to consider the lumped capacitance , inductance and resistance of a human body and by experimentson, I landed on about 70 nF or a self resonant frequency of approx 8 MHz.

I then considered what size of a physically large object that is notcontiguous with physical earth ( as in, a grounded object sunk into our Earth), or to mains safety earth, that would constitute an effective RF earth.

Custom would have it that any object suspended in space would not constitute an earth, (bird on EHT AC transmission line supported by a pylon, typically) but intuitively I feel this is wrong for RF conditions. I feel that a metal sphere of volume X at height H above our physical Earth would be a conductor under some conditions, even if not DC.

Interesting to hear your thoughts !

[G6Tanuki]

I always considered an average human standing on conductive earth to constitute a rather lossy 1/2-wave vertical VHF antenna.

Was interesting to ponder the possible current distribution when dealing with body-worn two-way radios working on 83MHz.

[G8HQP Dave]

I would expect the average adult to have a broad resonance somewhere around 50-60MHz. If well grounded at one end then about half this frequency.

You would need to be clear what you mean by effective RF earth. The required size would depend strongly on frequency, and weakly on things like conductivity and shape.

[Terry_VK5TM]

Not directly related to RF, but there are various definitions of body capacitance and other related things:-

The Human Body Model for capacitance, as defined by the Electrostatic Discharge Association (ESDA) is a 100pF capacitor in series with a 1.5kΩ resistor[1]

[1]https://www.esda.org/assets/Uploads/...ntalsPart5.pdf

I have seen one for RF, but can't find it at the moment (bad memory cells )

[Boater Sam]

The recent post about a flue and burner becoming "live" due to RF from a nearby aerial is a case in point. No deliberate earth was connected.
There was much discussion about induced RF from mobile phones affecting the brain, notice that modern phones transmit lower strength than some old classics.
Is the relation of wavelength and the size of a human body a relevance?

[Hartley118]

An interesting question Al.

I suspect that capacitance is the main parameter involved when we're looking at the human body. Electrically, I guess that we can think of the body as a bag of brine!

There's a pretty readable MIT lecture on a basic approach to capacitance at http://web.mit.edu/sahughes/www/8.022/lec06.pdf which might make some thought-provoking hospital reading. It includes interesting facts like:

* The dimension of capacitance is length
* A 1cm radius sphere has a capacitance of 1pF
* The capacitance of the earth works out to 0.0007F or 700uF

Martin

[GrimJosef]

Originally Posted by Hartley118

... I suspect that capacitance is the main parameter involved when we're looking at the human body ...

Yes. The subsidiary question is "Capacitance relative to what ?". Highly isolated objects like planet earth have a capacitance relative to points at infinity. We can work out this same capacitance for the human body and it will turn out to be small. But sometimes we are interested in electrical (strictly speaking electrostatic) pick-up relative to earth, typically when the source of the electric field has one terminal earthed and one 'hot'. Then the extent of any pickup by a nearby human will depend on the capacitance between the human and the hot terminal and also on the capacitance between the human and earth. Essentially we will have a capacitative divider. If we want to make the pickup small we should make the first capacitance small and the second one large.

Cheers,

GJ

[G8HQP Dave]

Originally Posted by Hartley118

The dimension of capacitance is length

I'm not certain it actually says that. In esu units it may appear to be length, but I suspect there is a conversion constant which just happens to be equal to 1, with hidden units.

[GrimJosef]

Capacitance is generally defined as charge divided by voltage. Capacitance really could have the dimension of length provided voltage and charge were defined such that their ratio was that of length.

A quick Google tells me that the definitions in cgs (the parent system of esu) and in SI are different https://en.wikipedia.org/wiki/Centim...ectromagnetism. The suggestion is that by taking the Ampere as a base unit of the system SI does introduce a hidden constant of proportionality (the vacuum permittivity). I've not had time to check whether cgs does though. Maybe it doesn't and capacitance in cgs really does have the dimension of length ?

Cheers,

GJ

[kalee20]

It's a hypothetical question really, but to be an effective earth yet not connected to earth, it would need to be rather big!

The radius of the moon is 1700km and this gives it a capacitance (relative to points at infinity) of about 200uF.

If you had a 50Hz AC fault current in a metal-cased appliance but the 'earth' lead from the metal enclosure went to the (isolated) moon and not to our planet, then you could pump about 3A before you started hitting the SELV limit of 50V. The Earth itself of course would be moving in antiphase, but being bigger, the capacitance would be bigger and amplitude would be less.

If you pulled hard on the grounding lead and dragged the moon closer, then the assumption that each body could be considered in isolation becomes less valid and direct capacitance between them starts to kick in, which would help things. But let's not go there, calculations become harder!

[Al (astral highway)]

Interesting replies, thank you everyone. I suspect that a hollow sphere, suspended ten metres above the earth, could be an RF ground, if it were large enough. I imagine that one of say 10m diameter would be meaurably effective. Of course , the sphere could end up with a negative or positive charge for a variety of reasons.

Clearly , the skin of an aeroplane, moving quickly through cloud spaces of widely divergent potential difference can be a RF earth and hence be struck by lightening .

I just wonder what is the smallest sphere that could act as a ground and at what distances above earth.
.
When I re-start my project , I will have to decide whether to shield all sensitive consumer electronics TV, Mac, you view box) or whether to unplug them from their Walwarts (proximal end, closest to appliance, leaving plug and SMPs detached ). They will then float to an indeterminate voltage above my RF ground and I can put a shifting mechanism across the SMPS (disconnected) end of the input from the detached SMPS and return that to safer earth.

[Hartley118]

SI units, unlike cgs units, do need to introduce the 'fiddle factor' of the 'permittivity of free space', which is 8.85x10exp(-12). Its unit is Farads per metre, which converts the capacitance length dimension into more familiar Farads which work with other useful SI units such as amps and volts.

The old cgs electrostatic units (ESU) are very 'pure' and consistent. They don't involve any fiddle factors, but are inconvenient in electrical circuits. For example, 1 ESU of potential difference is (nearly but not quite) 300V, whilst 1 ESU of current is approx 333 uA.

Martin

Martin

[G8HQP Dave]

I suspect that a hollow sphere, suspended ten metres above the earth, could be an RF ground, if it were large enough. I imagine that one of say 10m diameter would be meaurably effective.

As I said, it all depends on frequency, and what you mean by RF ground. At microwave frequencies people use local PCB 'grounds' which look rather like fanned-out quarterwave counterpoises. These may be only a few mm in length.

Clearly , the skin of an aeroplane, moving quickly through cloud spaces of widely divergent potential difference can be a RF earth and hence be struck by lightening .

You seem to be talking about three different things:
- acquiring an electrostatic charge
- being hit by a moving lump of charge
- providing a low impedance (to what?)

I just wonder what is the smallest sphere that could act as a ground and at what distances above earth.

Frequency? What is meant by "RF ground"? I keep coming back to these questions because they lie at the heart of what you are asking. If by "RF ground" you mean 'low RF impedance to the Earth' then even the Earth is not a good RF ground as soil/rock etc. is a poor conductor. If you mean 'effective as the other terminal of a monopole antenna' then a quarterwave piece of wire is fairly effective and four of them (going off in different directions) are very effective.

Originally Posted by Hartley118

The old cgs electrostatic units (ESU) are very 'pure' and consistent. They don't involve any fiddle factors, but are inconvenient in electrical circuits.

They may be pure and consistent, but only when you are dealing with purely electrostatic problems. As I said, I suspect that they hide a fiddle factor. Dimensional analysis should not depend on a system of units, so capacitance either has the dimensions of length or it does not. I suspect it does not.

If you take a 1/4 wavelength stick it will appear to be near zero ohms (50 ish as hinted at above) at the end you are holding it. The earth (as I seem to recall) is about 1 Farad and you can get a Farad in about a 1/4" cube these days, space is very big indeed!

[GrimJosef]

Originally Posted by G8HQP Dave

Dimensional analysis should not depend on a system of units, so capacitance either has the dimensions of length or it does not. I suspect it does not.

Dimensional analysis depends on definitions. If we define, say, the thing we call voltage in esu to be fundamentally different (i.e. having a different dimension) from the thing we call voltage in SI* then the capacitance, which is charge/voltage will have different dimensions in the two systems.

As someone once said "That's the nice thing about standards - there are so many to choose from".

Cheers,

GJ

*I was brought up never, ever, ever to use any system other than SI. Using multiple systems results in your spacecraft crashing at speed into the surface of Mars instead of landing on it. Or your patient being given a fatal overdose or next to no drug at all.

[G8HQP Dave]

Originally Posted by GrimJosef

Dimensional analysis depends on definitions. If we define, say, the thing we call voltage in esu to be fundamentally different (i.e. having a different dimension) from the thing we call voltage in SI* then the capacitance, which is charge/voltage will have different dimensions in the two systems.

If words have different meanings in different systems then anything is possible, apart from good science. The concepts of charge and voltage are surely well-defined, whatever system of units is used to count them. Hence the ratio of charge and voltage ought to be well-defined. Now it could turn out that this ratio really does have the dimensions of length, but I am not convinced.

There are examples in physics of two quite different concepts having the same dimensions. One is 'action' and 'angular momentum'. Whether this shows a deep connection between them is above my pay grade.

[Refugee]

I can remember seeing historic documents showing capacitance measured in Jars.
The press in this day and age would do all they can to quote the value in swimming pools as that is there standard unit for everything else.

[GrimJosef]

Originally Posted by G8HQP Dave

... The concepts of charge and voltage are surely well-defined, whatever system of units is used to count them. Hence the ratio of charge and voltage ought to be well-defined. Now it could turn out that this ratio really does have the dimensions of length, but I am not convinced ...

The system of units is not just about counting I'm afraid. It does include the very definitions which allow things to be 'well-defined'. The definitions are completely consistent within each system of units. They just differ between the systems.

In SI electric charge is an independent physical quantity. It can't be defined in terms of the base units length, mass and time. But in esu things are different and electric charge is not an independent physical quantity. It's perfectly well-defined and it can be dimensioned in terms of L, m and t. The dimensionality is given in the last paragraph of this section https://en.wikipedia.org/wiki/Centim...tic_units_(ESU).

I'm afraid that whether we're convinced by all of this isn't really material. We drive on the left in this country and on that basis I could say that I'm not convinced that the French drive on the right. But in France things are different and they do .

Cheers,

GJ

[Hartley118]

Originally Posted by Refugee

I can remember seeing historic documents showing capacitance measured in Jars.
The press in this day and age would do all they can to quote the value in swimming pools as that is their standard unit for everything else.

From early Leyden jars - favoured in the Admiralty Handbooks

1 jar = 10m

1uF = 900 jars (though there are more compact ways of achieving it )

Martin

[Neutrino]

Capacitance expressed in terms of SI base units is: m^−2 kg^−1 s^4 A^2
(Sorry, I do not see how to do superscript text here.)

The symbols for the SI base units are: m, kg, s, A, K, mol and cd. Even if you used other base units the relationships would be the same except perhaps for numerical factors. For example:

Capacitance (symbol F) expressed in terms of other units: C/V
Electric potential difference, electromotive force (symbol V) expressed in terms of other units: W/A
Power, radiant flux (symbol W) expressed in terms of other units: J/s
Energy, work, amount of heat (symbol J) expressed in terms of other units: N m
Force (symbol N) expressed in terms of other units: m kg s^-2
Electric charge (symbol C) expressed in terms of other units: s A

The SI Brochure is here:
https://www.bipm.org/en/publications/si-brochure/

David