I'd normally post this kind of thing in an image-board but this time i'd like some actual intelligent answers so here goes.

Theoretical question:

What if we were to take a 9 volt battery and attach one terminal to a copper wire aaaand pull the wire across the cirumference of the earth (like in the picture) and then measure between the end of the wire and the other terminal of the battery with a voltmeter.
Theoretically we Should read 9 volts right?
Let us for a minute imagine that we can actually do this in practice.
What will the actual reading be?
Will it be all over the place due to the inductance ? Will there be some kinds of losses? Some errors due to some electromagnetic or whatever
phenomena?

 

Why use a 9V battery? The effect of the battery voltage will be insignificant compared with the electrical signal that will be induced in the wire.

 

The way you have drawn the circuit, the voltmeter will give you a voltage of 9V DC.

I looked up the resistance of AWG10 copper wire and came up with 3.3Ω/km. A loop around the earth is about 4 x 10^7 m so the resistance is about 132kΩ. But the resistance is open-circuit and no current flows through it - so you still measure the battery voltage.

You could connect the wire to the other terminal and measure the voltage across it. It would still be 9V DC (the battery's internal resistance is negligible).

The loop might have some inductance, but this is not relevant for a DC current. It doesn't effect the impedance at DC.

The loop might have some magnetic fields flowing through it, but the fields are not changing so there is no induction. I am assuming that the loop doesn't move and that there are no fluctuations in the earth's magnetic fields - or nothing significant anyway.

But what if you replace the battery with an AC supply? What if you measure AC and DC voltages?

 

Yeah that's what i've been thinking , that the voltmeter should theoretically read 9volts because there is no current flow and no losses
But i'm interested in what effects the earths magnetic fields would have assuming the wire passes through the north and south poles and the measurement takes place at the equator for example .
And if there are any other phenomena similar to the m.fields that would affect the values .
Also Would this work at infinite ranges? I mean If we were to extend a loop of wire a few light years long lets say in a theoretical vacuum or without any external influences would the same ohms laws and other laws apply?

I Mean we know that at quantum levels the laws are completely different to those of newtonic , but what about at Yotta and Zetta and above?

This is probably a silly question , but i'd like to hear what people think about this nevertheless

 

There are losses in the wire (it is a 132kΩ resistor) but there is no current flowing through it, and hence no drop in potential, because it is open circuit.

It is only a changing magnetic field that induces a current. If the wire does not move through the earth's magnetic field or the magnetic field does not vary then there will be no induced current.

If you are trying to detect changes in the earth's magnetic field then you need to look for the small AC currents generated in the loop. You would not need to generate the DC current from the battery.

I think the same laws will apply for a very large loop - I cannot see why not. But if your loop is not fixed to the earth, then the earth can move past it or through it. The earth's magnetic field would induce a current in the loop. It would be like a giant generator.

 

I think current will be induced in the wire from three possible sources:

1) Man made EM radiation - power lines, radio transmitters, HAARP, etc.

2) EM radiation from Earth

3) Solar, interstellar and intergalactic EM radiation

 

I think with a giant antenna wrapped around the earth and a 9v battery in series with it, you would read wildly fluctuating voltages (combined all radio stations, solar flares, etc) ,with an indistinguishable +9v level shift.

 

Thanks to mikeleeson for doing the math. Thanks to strantor for mentioning the antenna effects.

A long wire is the old fashioned way to make an antenna for an AM radio. Your around-the-earth wire would make a good antenna, but you can take those signals out with a capacitor across the battery.

If you have a 10 megohm Fluke volt meter, like I do, the 132k of resistance would cause an error from 9.00 volts of 1.32%

There is no point in talking about infinity length because it can't happen and the math to show the error in the voltage has already been presented. Infinity length will cause an error from 9 volts of infinity, so the volt reading would be zero, give or take all the noise it picks up.

I don't see how a vacuum or quantum effects have any effect on this.

 

I tried to work out the inductance, but didn't get a sensible answer, maybe I messed up or the formula doesn't work for quite large loops.
From wikipedia : http://en.wikipedia.org/wiki/Inductance

Circular loop[16]

The answer I got was −133.9H (yes that is a minus sign)

<ed> just recalculated using a=1mm which I just found out is the radius of the wire, not the area of the loop.
I now get 181H
</ed>
<ed2>This is for an air core, so not really applicable to the Earth <ed2>

 

Given the earth is iron it would be much, much greater.

 

The way you have it wired in the image the DMM won't read anything at all. In order to measure voltage, the DMM should not be in series, it should be in parallel.

 

Infinity length will cause an error from 9 volts of infinity, so the volt reading would be zero, give or take all the noise it picks up.

I don't see how a vacuum or quantum effects have any effect on this.

I guess that makes sense , thanks for the input

 

The way you have it wired in the image the DMM won't read anything at all. In order to measure voltage, the DMM should not be in series, it should be in parallel.

But it is in parallel
Imagine the copper wire as an extention of the 9V battery terminal

 

I tried to work out the inductance, but didn't get a sensible answer, maybe I messed up or the formula doesn't work for quite large loops.
From wikipedia : http://en.wikipedia.org/wiki/Inductance

Circular loop[16]

The answer I got was −133.9H (yes that is a minus sign)

<ed> just recalculated using a=1mm which I just found out is the radius of the wire, not the area of the loop.
I now get 181H
</ed>
<ed2>This is for an air core, so not really applicable to the Earth <ed2>

This is exactly why I posted this question. It's hard to believe that these effects apply at such large scales . For example the earth acting like a ferromagnetic core to a wire wrapped around it

Thanks alot for the input

 

But it is in parallel
Imagine the copper wire as an extention of the 9V battery terminal

That would make sense if the wire had 0Ω resistance. However, having it go around the earth, the resistance will be quite high, creating a load. So it would be like connecting a resistor and DMM in series.

 

That would make sense if the wire had 0Ω resistance. However, having it go around the earth, the resistance will be quite high, creating a load. So it would be like connecting a resistor and DMM in series.

Yeah but we are measuring Voltage here and since the DMM has an input impedance of >10MΩ and we are using it as a voltmeter then we assume no current flow because it's in effect an 'open circuit' .

It would be the same thing as in the picture

z

 

Yeah but we are measuring Voltage here and since the DMM has an input impedance of >10MΩ and we are using it as a voltmeter then we assume no current flow because it's in effect an 'open circuit' .

It would be the same thing as in the picture

zView attachment 55731

Yup, you're right. My mistake