# Planet Earth and grounding a charged object

Discussion in 'General Electronics Chat' started by Spacerat, Sep 20, 2015.

1. ### Spacerat Thread Starter New Member

Aug 3, 2015
19
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Hello Forum,

Now lets consider a charge conductor carrying charge Q_initial=+1C and planet Earth.

Planet Earth can be considered to be a huge spherical conductor of radius 6,371 kilometers that carries a negative surface charge density of about -1 nC/square meter and capacitance ~ 710 microfarad. the Earth's surface is 510.1 trillion m² which implies that its total negative surface charge is 5.7*10^5 C. Lots of negative charge!

When we ground a charged object, the object and Earth becomes a single equipotential conductor that has the same electric potential V_equilibrium at every point. Charge will move around from high potential to low potential and distributes itself until a new equilibrium potential is set. The equipotential system (object+Earth) will carry a net negative charge since (Q_object+Q_earth ) ~ Q_earth. The highest negative surface charge density, but the smallest amount of charge, will be found on the "discharged" object which in reality has some charge and does not really get discharged at all.
In fact, regardless of the sign and amount of its initial charge, a charged object that is grounded will eventually carry a small amount of negative charge and will not become completely discharged.
Capacitance is C=Q/V and for Earth C is only 710 microfarad. But the earth charge Q_earth (5.7*10^5 C ) is so huge that V_earth=Q/C does not change much at all when it is connect with a charged object, i.e. when Earth receives or gives away a little amount of charge. After grounding, the equilibrium electric potential that the grounded object+Earth have is very close (equal for all practical purposes) to the initial Earth's potential V_earth=(9*10^9)*(5.7*10^5 C )/(6,371*10^3) (relative to infinity where V is set to zero).

Since it is potential difference is the quantity that matters, we often set V_earth=0 instead of using a point at infinity...

Are my observations correct? A grounded object, no matter its amount and sign of charge, does not get completely discharged and the earth potential is not affected (much) and remains constant...

thanks
Spacerat

2. ### peter taylor Member

Apr 1, 2013
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I would imagine that the earth could suck up trillions of volts of charge.

3. ### crutschow Expert

Mar 14, 2008
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You don't really care whether the grounded object is at some absolute zero potential, only that its charge is the same as the earth, whatever minute potential that is (relative to what, outer space?).

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4. ### BR-549 Well-Known Member

Sep 22, 2013
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I believe you are correct on your observations, but incorrect that it matters. Do you believe the earth will repel a small negative charge? One nano C is a lot stronger than one electron. Will the earth accept one electron?

The earth does not have a net charge. The charge that is detected, isn't because of charge imbalance. It's because electrons move around much more freely than protons, that's all.

Both positive and negative charge comes from the sun constantly. That keeps the earth neutral.

5. ### Spacerat Thread Starter New Member

Aug 3, 2015
19
0
What I read is that the system Earth+atmosphere is electrically neutral. But there is an electric field pointing downward (toward negative charge) in the air. The Earth+atmosphere act like a huge spherical capacitor.

As far as my grounding question, I have asked it because I am trying to understand what happens when a AC voltage source has one of its terminals connected to Earth (i.e. grounded). If the AC source is not grounded its two terminals A and B will have sinusoidally changing potential difference. We don't know the value of either potentials, V_A and V_B, but we know their instantaneous difference (V_B- V_A) in time.
It could be that both V_A and B_B change in time.

If we grounded either one of the AC source terminals, say terminal A, then I believe V_A remains fixed, constant in time (assume the same potential as planet earth), while V_B oscillates about V_A.

An AC source acts like an oscillator that moves charge from one terminals to the other: when one terminal has charge +Q the other has charge -Q causing different potentials on the terminals. This happens also when one of the terminals is grounded but its potential does not change, as said above, because it is connected to planet Earth.

I am just trying to see if my understanding is correct and need some validation...

thanks to everyone!

6. ### BR-549 Well-Known Member

Sep 22, 2013
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The earth/atmosphere is a lot more than a cap. There are many alternating electric fields and magnetic fields in this interface. Modern science is just at it’s infancy at studying this.

I think using ground for a leg of AC is like turning off half of your AC source.

In many applications, we only want or need half of the AC source.

It depends on the AC context......power or pattern or other.

7. ### AnalogKid Distinguished Member

Aug 1, 2013
4,685
1,297
Pretty sure I disagree. If we are talking about a floating AC source like the output of a generator, the instantaneous potential differences between AC1 and AC2 (no positive/negative designations) and the RMS value of the source are the same no matter if either end is "grounded", tied to one end of a 12 V car battery, or whatever. That's the fun thing about floating sources. This is like stacking two fully isolated 5V power supplies together to make a 10 V source.

Note that in standard US domestic power service, 240 VAC with a center-tapped neutral, the instantaneous values of both phase legs oscillate plus and minus about the neutral. It is the phase difference between the legs that creates the higher voltage at the load. IF the neutral is connected to earth ground and IF a load intended for both phase legs is connected to only one leg and ground, THEN it is receiving half the intended power. But that is a wiring error, not a general statement about the characteristics of multi-phase AC power distribution.

IMHO.

ak

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8. ### crutschow Expert

Mar 14, 2008
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Not true.
Whether one leg of a AC source is grounded to earth or not has absolutely no effect on the voltage or the waveform characteristics between the two legs.

9. ### wayneh Expert

Sep 9, 2010
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I don't see how one leads to the other. Why couldn't there still be an imbalance? Is the flow from the sun balanced, on the whole?

Sep 18, 2014
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11. ### john*michael Member

Sep 18, 2014
43
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This is a really important subject, and I can’t stay out of the discussion!

First of all, the earth is not a conductor, and the surface of the earth is not equipotential. Earth formations have varying resistivity and dielectric constants depending on the soil content. The voltage difference between different locations on the earth’s surface is measureable; in the oil exploration business we often impress voltages between differing points, sometimes miles apart, to signal to downhole instruments or to take measurements. At any given point, different places on the earth have widely varying voltages, so anything we designate as ground is really only for our own reference.

The term “ground” is used by us electronics folks for many purposes. But for the purposes of this discussion, we choose to tie one side of our AC power to earth ground for safety reasons. If we build equipment with the chassis tied to this earth ground, and something goes wrong inside so that the high voltage (not grounded) side touches the chassis, it will short out the circuit. If we leave the chassis floating and this occurs, the chassis would be hot (although the device would probably still function) and if someone touched the chassis while also touching another, properly grounded object, they would get a jolt. Many of us have personal experience with this phenomenon!

We generally tie ground to the actual earth for the same reason; in the event that the earth is conductive (maybe a puddle or water in a bathtub touching the plumbing) we want to make sure that the non-grounded side of any circuit that comes into contact with the ground will be shorted out.

This is the reason that two-pronged plugs have different-sized prongs, and the reason that three-pronged plugs exist – so we won’t have an option to get the high side and ground reversed. If a device has a plug with two identical prongs, it must be double-insulated to provide extra protection against shocking the user.

Anyway, your understanding about what happens when you connect one side to ground is absolutely correct; you can either have a grounded AC voltage that has one side oscillate as a sinusoid about ground, or you can have it float wherever you want it. For example, you could take an isolation transformer and attach one side of its AC output to a 500-volt DC power supply referenced to ground. 120 VAC would still be measured between the isolation transformers output terminals. But if you put a scope on it (referenced to ground), the sine wave would swing positive and negative about 500 volts.

12. ### Kermit2 AAC Fanatic!

Feb 5, 2010
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The Earth most certainly IS a conductor. It is not a good one like copper but it IS a conductor. Now that we have a world spanning electric grid it has become a very important conductor in relation to it.

Actually EVERTHING is a conductor and it is the degree of effort by which an electron moves which spawns our use of the term "electrical insulator". Exactly the same as there only being more or less heat in a system which spawns the term "cold" to describe a relative absence of heat. There is no cold, and there is no insulation, per say. There is only more or less heat and only more or less electrical conduction. The other words are human constructs to denote a degree or amount of those things.

13. ### BR-549 Well-Known Member

Sep 22, 2013
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It’s the context gentlemen, we’re talking about a whole lot of different things now.

You can relate many things and ignore many things depending on your point.

14. ### Wendy Moderator

Mar 24, 2008
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There are places in the world that uses the earth as one of the conductors. Kinda dispels the earth not being a conductor. Some areas are less conductive than others, but people regularly die from electrocution from standing on the earth and grabbing a hot wire.

15. ### BR-549 Well-Known Member

Sep 22, 2013
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I think the earth is a sork. A sork is a device that can both sink and source either/both charges.

16. ### john*michael Member

Sep 18, 2014
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Exactly the point Spacerat is making. If you touch a hot wire you will be shocked only if the other side is grounded; otherwise, if both sides are floating, you will not be shocked unless you get both wires.

17. ### BR-549 Well-Known Member

Sep 22, 2013
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Wow.........I wouldn't try that! Danger Danger Will Robinson.

18. ### Wendy Moderator

Mar 24, 2008
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Not legal in the USA, but then, it isn't in the USA. I find the concept of electrical losses being cheaper than wire... interesting.

In the USA, and most the world, Neutral is always connected to ground. Always.

19. ### john*michael Member

Sep 18, 2014
43
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Not Recommending with line power! But you actually do this every time you handle battery cables in your car. You can leave either cable on laying on the ground without generating a spark, but if you touch them together... The tires act as an insulator (or extremely poor conductor for Kermit2) and keep both battery terminals floating. On the other hand, most cars have the chassis grounded to the negative terminal, so you can't touch the positive to the engine block.

20. ### wayneh Expert

Sep 9, 2010
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3,226
Good point. What do we call empty space? We would normally call it an insulator but once you send an electron moving through it, it's a superconductor since there is nothing to stop that electron. Hmmm....

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