Voltage between two points on an empty wire

[sophiecentaur]

you said that the reference is infinity, so the source of electric field is at infinity?

That doesn't follow at all. The reason that infinity is used as a reference 'point' is that the choice is entirely arbitrary but infinity works wherever you happen to be. Could you think of a more suitable place? The Inverse Law (1/R) would make it inconvenient to use zero as an origin. Having rejected that, you could choose my front gate or the top of Mount Fuji but the French would surely argue with those choices. Infinity is a very suitable choice as its the same for everyone - even the inhabitants of Planet Zog. In any case, we are nearly always concerned with changes in potential between different points (gravitational or electric).
"Voltage" is a very sloppy terms that we all tend to use for Potential Difference but, on its own, it's often used to refer to the Potential Difference between our point of interest and 'Earth' - perhaps the metal pipes in your house or a metal spike / mat in the Earth outside. A Voltmeter always needs two connections and it always measures Potential Difference.

 

[cnh1995]

According to my understanding in point 3-, voltage is different from potential difference

See this recent featured thread.
https://www.physicsforums.com/threads/tiny-tweak-in-teaching-basic-circuits.908496/

 

[davenn]

3- We must measure potential difference to know the actual work that's done by the running electrons in the circuit. If we want to measure potential difference between points A and B, then we measure voltage at point A (which is caused by some excess of electrons at point A), then we measure voltage at point B (which is caused by some lesser or greater excess of electrons), and then we subtract the two measurements to determine the direction and work of the running electrons in the circuit

not really, no
we measure the voltage (PD) BETWEEN points A and B, they are not measured and cannot be measured separately, BECAUSE we are measuring the difference between them
So in your diagram you posted at the start

you put the negative probe of your meter on 1 (A) and the positive of your meter on 2 (B) and you measure the voltage drop between those points
you could then put the negative probe of your meter on 2 (B) and the positive of your meter on 3 (C) and you measure the voltage drop between those points in this case across the globe)

voltage needs (must) to be measured between TWO points. You CANNOT say that the voltage at point 1 or 2 or 3 or 4 is xx volts without it being referenced to somewhere else in the circuit

Also a way back you couldn't understand why you couldn't measure a voltage between 1 and 2
if as stated it is an ideal wire ( no resistance) then the voltage (PD) measured between those 2 points will be zero ... why ?
V = I x R
V = let's say 2 Amps x 0 R
2 x 0 = 0 therefore V = 0 (zero)

real world, that length of wire will have a resistance depending on its length and conductor size and as a result there will be a small measurable voltage drop

4- According to my understanding in point 3-, voltage is different from potential difference

no, because as I said above you CANNOT measure a voltage (PD) without relating it to another point in the circuitDave

 

[jim hardy]

After a while I came to a layman's understanding. Here it is:
1- Any excess of electrons causes potential energy
2- Voltage is potential energy per unit charge, so voltage is potential energy
3- We must measure potential difference to know the actual work that's done by the running electrons in the circuit. If we want to measure potential difference between points A and B, then we measure voltage at point A (which is caused by some excess of electrons at point A), then we measure voltage at point B (which is caused by some lesser or greater excess of electrons), and then we subtract the two measurements to determine the direction and work of the running electrons in the circuit
4- According to my understanding in point 3-, voltage is different from potential difference

Maybe that's enough for diving in electronics. What's your say on this? I'm eager to hear, because all my understanding may be nonsense.

It is so difficult to take the picture one has in his own mind and use words to paint that same picture in someone else's mind .

Let me take your words one thought at a time.

1- Any excess of electrons causes potential energy
Okay, in the sense that electrons in proximity to one another and absent any positive charges to ameliorate their natural coulombic repelling force , if something constrains them there is potential energy due to those coulombic forces.

2- Voltage is potential energy per unit charge, so voltage is potential energy
Potential energy per unit charge. Joule per coulomb or electron volt per electron. Look up the conversion from ev to J and see what other constant it resembles.

3- We must measure potential difference to know the actual work that's done by the running electrons in the circuit. If we want to measure potential difference between points A and B, then we measure voltage at point A (which is caused by some excess of electrons at point A), then we measure voltage at point B (which is caused by some lesser or greater excess of electrons), and then we subtract the two measurements to determine the direction and work of the running electrons in the circuit
I can't accept that one.
Voltage is potential difference, go back to my first post.
Difference implies two points between which you have a difference. That's why voltmeters have two wires, usually one red and one black.
oops company just arrived got to go will finish later.

looks like Dave may have done the job for me !

jim

 

[jim hardy]

3- We must measure potential difference to know the actual work that's done by the running electrons in the circuit. If we want to measure potential difference between points A and B, then we measure voltage at point A (which is caused by some excess of electrons at point A), then we measure voltage at point B (which is caused by some lesser or greater excess of electrons), and then we subtract the two measurements to determine the direction and work of the running electrons in the circuit
I can't accept that one.
Voltage is potential difference, go back to my first post.
Difference implies two points between which you have a difference. That's why voltmeters have two wires, usually one red and one black.
oops company just arrived got to go will finish later.

"We must measure potential difference to know the actual work that's done by the running electrons in the circuit."
That part is true.

"If we want to measure potential difference between points A and B," then we simply measure the voltage between those two points with our two wire voltmeter..
" then we measure voltage at point A (which is caused by some excess of electrons at point A), then we measure voltage at point B (which is caused by some lesser or greater excess of electrons), and then we subtract the two measurements to determine the direction and work of the running electrons in the circuit"
That indeed is the thought experiment i described , remember all my hyperbole about Alpha Centauri. If you have a voltmeter with one wire long enough to reach Alpha Centauri then you could do that
You're still thinking about absolute voltage oops edit: make that absolute potential which is an important concept to understand but completely impractical to measure. We have to settle for potential difference between two points that we can get to.

And, you're homing in on the concept. This takes time , and when it "clicks" you will be unable to even remember when it wasn't intuitive.

So Hang In There
and be tolerant of my picayune nitpicking. It is important to get these fundamentals straight lest you build on a false foundation.

The gravity analogy is useful, as is the water analogy. but there's a danger in both.
They cause one to think charge is somehow attracted to earth, that electricity has some affinity for ground.. Of course our childhood memories of lightning and rain reinforce that misconception and it becomes accepted as the fact it is not, and we become more confused as we build on that false premise.

Your next step is to form the habit of ALWAYS saying "voltage between (A) and (B), NEVER "Voltage at A or Voltage at B" . As Dave said .

the sciences have made progress, because philosophers have applied themselves with more attention to observe, and have communicated to their language that precision and accuracy which they have employed in their observations: In correcting their language they reason better.'

 

[sophiecentaur]

This takes time , and when it "clicks" you will be unable to even remember when it wasn't intuitive.

This is such an important point. People who claim not to have an "intuitive" feeling about a topic and that it "doesn't make sense" seem to assume that they were actually born with the ideas they are using at the time. As far as I am aware, there is no intellectual process that we are actually born with. All we start with is the basic tools for us to process such things. All the rest is learned and acquired during our lives. The time that people spend in trying to justify a badly informed position would be much better spent in using the combined wisdom of history to bring themselves up to speed with the conventional views. IFF they happen to be a genius like Newton, Einstein, Pauli etc. then they may later be in a position to challenge those ideas and make a change to the textbooks. Personally, I reckon that those guys didn't mess about, challenging well established stuff. They went along with it, until they knew it forwards, backwards and sideways and then got on with altering history.