Earth's electric charge

[khushi]

Earth has a charge of -1.6×10^-19C or about 7 moles of excess electrons on it's surface. This is compensated by an equal deficiency of electrons in the Earth's upper atmosphere.
Earth is also an infinite source and sink of current.
Now, when current flows into it, that means it loses electrons. So, to create balance, the upper atmosphere should also gain the same amount of electrons. How does that happen?

 

[mfb]

Earth is also an infinite source and sink of current.

It is not.
Current that flows into it flows out again to an extremely good approximation. The only exception is a charge transfer between the atmosphere and the earth, where the answer to your question is trivial.

 

[khushi]

Oh okay yes, it has to flow out or else there won't be a closed circuit for current to flow. And i suppose it should be the same network, a part of which is touching the ground. Am I right? But when charging a metal ball by induction in which :-
An uncharged metal ball is supported on an insulating stand. A negatively charged rod is brought near it, causing charges to redistribute, with electrons pushed on the opposite side. So, if we connect a metal wire b/w the -ve end and gnd, the -ve charge flows into earth. So, we then remove the rod and the ball is +vely charged.
Now, where is the circuit in this?

 

[mfb]

And i suppose it should be the same network, a part of which is touching the ground.

With a single connection, you don't get relevant currents towards ground. You can make a small charge separation by putting some charge on a metal ball, yes. The sum of all charges of your lab experiment plus Earth will stay constant as charge is conserved.

 

[khushi]

But then the Earth would get a charge. And we can then remove the charged ball from the lab and the Earth will still have an extra charge. What about that?

 

[mfb]

If you shoot the charged ball to space, yes, you change the charge of Earth by a tiny amount.

 

[Dale]

Now, where is the circuit in this?

The charged ball is one "plate" of a capacitor. The other plate is ground. The current is the standard displacement current found in any capacitor.

 

[Khashishi]

-1.6×10^-19C is the charge of one electron, not 7 moles.

 

[khushi]

-1.6×10^-19C is the charge of one electron, not 7 moles.

Sorry, it's a mistake, total charge is -6.8×10^5 C, which corresponds to 7 mole of excess electrons.

 

[khushi]

The charged ball is one "plate" of a capacitor. The other plate is ground. The current is the standard displacement current found in any capacitor.

But how can it be a capacitor when the ball and Earth are connected with a wire? When we remove the wire, then it can be seen as a capacitor but the charge traveled to Earth during the time wire was connected.

 

[Dale]

Huh? Capacitors are usually connected by wires in circuits. That doesn't change anything. The connecting and disconnecting would be a switch, separate from the capacitor.