Is the Earth really electrically neutral (0.00000000V), or do we just say it is?

[TimFox]

From Wikipedia:
"The electroscope can also be charged without touching it to a charged object, by electrostatic induction. If a charged object is brought near the electroscope terminal, the leaves also diverge, because the electric field of the object causes the charges in the electroscope rod to separate. Charges of the opposite polarity to the charged object are attracted to the terminal, while charges with the same polarity are repelled to the leaves, causing them to spread. If the electroscope terminal is grounded while the charged object is nearby, by touching it momentarily with a finger, the same polarity charges in the leaves drain away to ground, leaving the electroscope with a net charge of opposite polarity to the object. The leaves close because the charge is all concentrated at the terminal end. When the charged object is moved away, the charge at the terminal spreads into the leaves, causing them to spread apart again."
Again, the external E field, applied to the entire device, induces a charge (monopole) on the metal guts, including the leaves, which then deflect by Coulomb force.  The excerpt above includes a specific procedure for discharge, which includes connection (finger) to the terminal.

[houkensjtu]

OT: I think the problem related with "earth" is really not simple for newbies, hoping Dave could make a "fundamental Friday" on this topic!

[Marco]

To clarify what I was saying about the Faraday cage: if you place the electroscope inside a Faraday cage and connect the electrode to the cage (local "ground"), then the electroscope will have no charge on it relative to its local environment

Oops, you're right of coarse ... the excess charge is on the outside of the cage.

[niconiconi]

Voltage is relative.  That's all there is to say!

Perhaps it would be more illuminating to think in terms of electric field, which produces the force on the electroscope.  Electric field is the spacial derivative (gradient) of voltage, so it has no absolute reference, the constant term disappears.  Likewise, voltage can be measured as the integral (along a given path) of electric field; the absolute voltage is the "plus a constant" of integration -- a free variable that doesn't matter to the problem, internally.

Tim

Sorry for bumping an old thread. I came across this thread while trying to find the answer to the same problem on the Web. After getting confused by it for several years, I think I have finally found the answer.

In engineering textbooks, voltage is always defined with respect to a reference, so engineering students believe all voltages are relative. Meanwhile, many physics textbooks on electrostatics say that an object's absolute electric potential is defined with respect to point at infinity for several reasons. So physics students believe an absolute voltage exists in some forms, at least in theory. In fact, it can be really difficult to analyze non-circuit problems in physics if you don't accept the existence of an absolute potential:

1. Imagine a single electron in a vacuum, the absolute electric potential at point A is the work required (with a negative sign) to overcome the electric force to bring a test charge from point A to a point at infinity without any electric field.
2. All objects are formed by subatomic particles, some particles like electrons and protons, carries an elementary charge, and it can be both polarities. Theoretically one knows the exact charge distribution of an object, it's possible to calculate its electric potential and electric field, with respect to point at infinity.
3. Like charges always repel, opposite charges always attract, and both charges always attract neutral objects, it's just Coulomb's law. Even two objects that have never met each other before, still apply electrostatic forces to each other - circuit theory doesn't allow us to analyze this situation but electrostatics can, with respect to point at infinity. Also, if you add charges to all objects to increase their potentials, the outcome of electrostatic experiments may change. This suggest one can detect charges absolutely in theory.

Even in engineering, absolute electric potential is sometimes used when there's no well-defined reference. For example the Human-Body Model of ESD said the human body's capacitance is a "free-space capacitance". In other words, the "self-capacitance" in electrostatics - it's the extra charges needed to increase the absolute electric potential of an object by 1 V. So accepting absolute potential gives you a wildcard when your reference is not well-defined - with respect to what? Just everything else, whatever it may be...

So is voltage absolute or relative, for real? It turns out that, after reading more physics... Ultimately, it's still relative. The trick is to consider what happens when you increase the electric potential of the vacuum itself together with all objects inside it, once you do that, the outcome of all electrostatic experiments remain unchanged. Coulomb's law works just fine. The electric field remains unchanged since the (static) electric field is the gradient of electric potential, and only E causes physical effects, so only the potential difference matters. Furthermore, it turns out that the entire theory of classical electromagnetism is known as gauge-invariant in theoretical physics. Adding a gauge transformation to the electric potential V or the magnetic vector potential A, does not change the observable electric field E and magnetic field B.

So TL;DR: Absolute electric potential exists, in a sense, using a far vacuum as the reference. Sometimes the concept is even useful too. But this definition assumes the electric potential of the "background" vacuum itself is 0 V - which is only a convention. One is free to choose other values.

To put it in another way, one can imagine the universe as a Faraday cage with Perfect Electric Conductor as its boundary condition. It's natural to define the cage itself to be at 0 V for simplicity, but in fact any voltage would do, since the potential of everything inside the cage increases by the same amount so it has no detectable physical effect - observers outside that cage will have different ideas about its electric potential as well.

Now here's the question I don't know yet... Is it possible to approximately measure the "absolute electric potential" defined by electrostatics experimentally? If not a point at infinity, at least a point at somewhere else in the solar system...

[bdunham7]

Voltages are all relative, right?

Voltage is only ever meaningful as a difference.

Voltage by definition is charge difference. Talking about the charge difference of one point is pointless.

These statements reflect a common understanding of how we usually think of voltage in practical circuits, but they are, in fact, incorrect.  Voltage and charge are inherently absolute values. 

[CatalinaWOW]

Voltages are all relative, right?

Voltage is only ever meaningful as a difference.

Voltage by definition is charge difference. Talking about the charge difference of one point is pointless.

These statements reflect a common understanding of how we usually think of voltage in practical circuits, but they are, in fact, incorrect.  Voltage and charge are inherently absolute values.

Still confusion exists.  Charge is an absolute value?  Yes the fundamental unit of charge is fixed, and charge of any defined region or object is just the count of those fundamental units contained in that defining box.  So absolute once your box is defined.  I don't see voltage as absolute in any sense.  Take a single electron in an otherwise empty universe.  Voltage can be thought of in many ways, but one obvious one is the difference in e field strength between two points.  So there is a unique voltage between the electron and the end of that empty universe.  But a different one between it and a point a few centimeters away. 

Thinking numerically would clarify some of the issues.  I haven't actually done the math, but I am sure that the ratio of positive to negative charges associated with the earth (defined as the region of space around us to some radius well beyond the moon) is one to a great many decimal points.  I am equally sure that there is a net surplus (or deficit) of electrons of a huge number of coulombs.  Depending on what you are doing one or the other of those facts will be more important.  The same two facts apply (with different numerical values) apply to the atmosphere.  And the existence of lightning indicates that the second fact is important even though the balance of positive and negative charges is nearly perfect.

[T3sl4co1l]

Note that voltage at infinity is indeterminate, and any choice is arbitrary.  Zero is perhaps the least arbitrary real number, so it's a common choice -- but it is still just as arbitrary

Tim

[TimFox]

Another way of stating the point above is that if you were to add, say, +100 V to the voltage at every point in the universe, it would make no physical difference, since the electrostatic field (E) that induces forces on test charges would remain the same.
However, you cannot arbitrarily add 1 Coulomb of charge to everything:  any given physical object contains a fixed quantity of charge carriers (electrons, protons, etc.) that add up to the charge on that object.

[Doctorandus_P]

The way I heard it explained, there is apparently a shortage of electrons in the universe, and as a result of that "stuff" will be positively charged. But I don't know how big this charge is. Apparently it's not very big, or those "goldleaf electrometers" (Mentioned 9 years ago in this thread) would always push their leaves apart.

And you have to consider the differenced between electrical charge and voltage.

Electrical charge is simply the difference between electrons and protons in some object, while voltages are always differentials, and thus you need two points to measure the voltage (differental) between those points.

[T3sl4co1l]

A volumetric charge imbalance in the universe wouldn't need to be very large for the energy level around any given (astronomical) volume to be so high as to rip balance charges out of the very fabric of space-time; although there's also no known mechanism I think for C parity violation in and of itself (i.e. creation of charge out of absolutely nothing)?  But by the same token, there's no reason the universe shouldn't be neutral since creation, nor remain that way.

Other than that, local regions can have charge, but they'll very quickly draw a balance toward them, and the inter{planetary|stellar|galactic} medium is, however tenuous, also filled with plasma and so is conductive over long enough time scales.  I would guess most low-density astronomical objects have on the order of GV on them, tops, and the more dense ones (neutron stars, black holes) can manage... somewhat more than that?  I don't think I've seen it discussed specifically but there'll be a charge loss mechanism by the same argument as Hawking radiation so even a black hole is not a perfect insulator.

Tim

[Nominal Animal]

Voltage [is] inherently absolute [values].

No, that's not correct either. Electric potential is an absolute value, yes; and so is charge.  But voltage is a purely relative measurement: the difference between two electric potentials.

It is easy to confuse electric potential (also called electrostatic potential) with voltage, because both use "volt" as the SI unit.

To put it crudely, if you point to some single thing, you can say it has Q coulombs of charge, and V volts of electrostatic potential; but you cannot say it has a voltage of V volts.

The original post from a decade ago is a good example of this confusion.
The short answer to that is "No, the Earth has quite a large electric potential", but a proper answer would also add "but since everything in the human scale tends to that same potential, it makes sense to choose that as the reference potential for voltage measurements: to compare any other electric potential against."

[iMo]

The way I heard it explained, there is apparently a shortage of electrons in the universe, and as a result of that "stuff" will be positively charged..

Let us wait on the ali and ebay sellers offering the electrons.. 

[RJSV]

   I would agree with that field strength, 200 V per meter
   What about capacitance ?   Regardless of accumulated charges, from solar wind, etc. the huge earth itself must have large capacitance, and accessable through a single connection.
   I learned that from watching the various ElectroBoom videos, on Tesla coils.   I learned, you CAN get a high voltage shock, having only the one wire or other conducting path.
Actually, thinking about that, a lightning strike is a form of 'single connection' (rather than a completed circuit loop.)

[radiolistener]

For any normal circuit it wouldn't matter.  And how would we know anyway?  Voltages are all relative, right?  Might the Earth not be truly neutral - it has some net charge one way or the other?

Yes, it may have some charge relative to other sky object. Depends on a reference, Earth charge may be positive or negative, or zero.

If we get Earth charge as a reference, then Earth charge will be zero because Earth charge - Earth charge = 0.

If we get average charge of entire universe (all objects) as a reference, Earth charge probably will be close to zero, but if there is balance between positive and negative charges in universe. But it is possible that there is some imbalance, and in that case Earth charge will not be zero relative to average universe charge. 

 Are all heavenly bodies neutral - or might there be a potential of difference between the Earth and the Moon or Venus?

it depends on the object which you select for comparison

[jmelson]

When I was in high school, I visited the local university physics department and the professor had an experiment in progress to measure the electrostatic field in the atmosphere at different locations.  The apparatus was a pair of electrodes with one rotating rapidly.  If I remember correctly, the top electrode was three 60-degree segments with 60-degree gaps, and the lower electrode had six 60-degree segments with short gaps.  In order to get a huge input impedance on the amplifier for the AC voltage produced by this sensor, he used an acorn triode (955) with the input connected between the plate and cathode and the output from the grid-cathode circuit.  He showed me how to clean the glass carefully to avoid parasitic resistance.

This is called a field mill, and the rotating shutters convert the static field into AC, so a high impedance op-amp can measure it.  There was an "amateur scientist" article on building one in Scientific American, but I can't find it now.  I did find this article:
https://www.google.com/url?sa=t&source=web&rct=j&opi=89978449&url=https://www.vaisala.com/sites/default/files/documents/Recent%2520Work%2520on%2520the%2520Georgia%2520Tech%2520High%2520School%2520Field%2520Mill%2520Project.pdf&ved=2ahUKEwjyrJqCt--GAxVAkYkEHQRLBfEQFnoECCsQAQ&usg=AOvVaw1xQt9JcPe1TUR-fsJWcJFs

Jon

[ejeffrey]

But an electroscope shows that, in fact, there IS such a thing as an absolute reference for zero volts, even though it may be hard to measure precisely.  A gold leaf electroscope is a crude sort of voltmeter, with only one terminal.

https://en.wikipedia.org/wiki/Electroscope

The two leaves of a gold leaf electroscope will separate if there is a positive voltage on them, and they'll also separate if there is a negative voltage on them.  Since they're conductive, they'll each have the same voltage, and since like charges repel, if there is a non-zero net charge on them, they will repel.  The two leaves will have no repulsive force between them only if they've got zero volts on them.

Zero volts would be when the body as a whole has no net charge, that is, the same number of protons as electrons.

No all of that is wrong.  There is no measurable "zero absolute potential" and that's not what an electroscope shows. 

An electroscope measures net charge, but if you want to consider it a voltmeter, it has two terminals.  The second terminal is the frame.

[Marco]

So lets say the earth has excess electric charge relative to the rest of the local universe, would most of the excess charge be in the upper atmosphere? (Similar to any charged conductor.)

And if the universe as a whole had a significant net charge it wouldn't be measurable, because solids would not exist?