# Anyone care to demystify ampere for the layperson?

1. Jan 6, 2006

### hkhil

Hello

This is a section from a textbook...

"an ampere is defined as that current in each of 2 infintely long parallel wires 1 m apart that causes an electromagnetic force of 2 x 10^-7 per meter of its length to act on each wire"

Hmmm... was that in English ?

q1. So say we start at 0. After 1 meter, wire 1 will cause a force of 2 x 10^-7 N (Is it in Newtons?) on wire 2.
That would mean that after 2 meters, wire 1 will cause a force of 2( 2 x 10^-7) N of force on wire 2... and so on.
Is that what that passage is trying to say?

If so... what does that have to do with anything? Considering we learnt that an amp is basically the number of electrons flowing past a given point per second.

2. Jan 6, 2006

### Staff: Mentor

Imagine two very long parallel straight wires, one meter apart, carrying equal currents. Ideally, you need infinitely long wires, but in practice it works well if you have very long wires (several meters?) and just look at the middle part of the wires. The reason for this is that the magnetic field produced by the wires is distorted at the ends because of "end effects", and we need to make those effects small enough to ignore.
Now take a one-meter section of one of the wires. If the magnetic force acting on that one-meter section is $2 \times 10^{-7}$ N, then the current through each wire is by definition 1 ampere. On a two-meter section of the wire, the force would be $4 \times 10^{-7}$ N, etc.
This seems like a strange way to define current. After all, electric current is a flow of charge, so it might seem more intuitive to define our unit of current in terms of some number of electrons per second. The reason we don't do this is that it's easier to measure forces and distances precisely, than it is to measure the precise amount of charge passing through a wire. Definitions of units have to be easily reproducible in a laboratory in a precise way.

3. Jan 6, 2006

### chroot

Staff Emeritus
Since this is not quantum physics, I am moving it.

- Warren

4. Jan 6, 2006

### hkhil

Hi JT

Thanks I got it now.

Last edited: Jan 6, 2006
5. Jan 10, 2006

### rcgldr

There's no reason not to define an Amp in terms of electrons per second:

$$1 \ amp \approx \ 6.25 \ \times \ 10^{18} \ electrons \ / \ second$$

Last edited: Jan 10, 2006
6. Jan 10, 2006

### ZapperZ

Staff Emeritus
The only problem with doing this is that "electron per second" has units of "number/s". One can get into quite a bit of a dimensional analysis mess if one doesn't actually realize that your "electrons" is meant as as "charge of electrons".

I certainly would not recommend doing this to anyone just starting out learning physics. There's nothing wrong with the standard definition, so why introduce an unnecessary ambiguity?

Zz.

7. Jan 10, 2006

### rcgldr

Ok, electron charges per second. Last I remember 1 amp was defined as 1 Coulomb per second, and a Coulomb is about 6.25x10^18 electron charges. In an ideal metal conductor, where the only flow is electrons moving from molecule to molecule, then electrons per second should be close enough for a lay person to understand.

Last edited: Jan 10, 2006
8. Jan 10, 2006

### ZapperZ

Staff Emeritus
Sure, but call it something else, such as "flux", which has a very flexible definition in various parts of physics. But you were attempting to change a very fixed definition that can cause a "lay person" to use it wrongly, which lay persons are apt to do.

Zz.

9. Jan 10, 2006

### rcgldr

The web site below defines 1 Amp as 1 Coulomb per second and defines an electron charge at 1.6^10-19 Coulombs, making a Coulomb 6.25x10^18 electron charges. It also goes on to state that you have electron flow in wires and ion flow in fluids.

When did the defnition of 1 Amp change from 1 Coulomb per second?

http://www.gcse.com/glos.htm

10. Jan 10, 2006

### ZapperZ

Staff Emeritus
When was it ever defined differently?

Zz.

11. Jan 10, 2006

### rcgldr

From the original post in this thread:

"an ampere is defined as that current in each of 2 infintely long parallel wires 1 m apart that causes an electromagnetic force of 2 x 10^-7 per meter of its length to act on each wire"

Now where can I actually measure the force between 2 infinitely long parallel wires? I prefer the mks standard of 1 coulomb / second.

12. Jan 10, 2006

### Galileo

You then still have the question of defining how much a Coulomb is. The point is that the Coulomb is defined in terms of the ampere.
The standard definition (force of the two wires) uses no new quantities, only ye old force which can all measure.

13. Jan 10, 2006

### Staff: Mentor

If all you want is a conceptual definition, then this will work fine, provided of course that you specify the number of electrons precisely, and you specify the amount of charge on an electron.

However, the official definitions that people actually use in the laboratory must be practical. How can one count electrons precisely, in practice?

For the same reason, we still define the kilogram as the mass of a specific lump of platinium-iridium alloy in a basement in Paris. People are working on ways to count atoms precisely, so that someday we can define a kilogram as a specific number of atoms of some isotope, but we're not there yet.

14. Jan 10, 2006

### ZapperZ

Staff Emeritus
No, look again. They're not that different. Use Biot-Savart Law and use dimensional analysis. They're identical. You can do the same thing with the electric field. You can define it in units of V/m, or N/C. Break each of them down to the fundamental units and you'll get the same dimensions. They are not different beasts.

But saying an Ampere is # of electrons/second is.

Zz.

15. Jan 10, 2006

### rcgldr

Isn't a Newton just as conceptual? After all it is the force required to accelerate that same lump of alloy in Paris 1 meter / sec^2. At least meter has been defined as so many wavelengths of a certain frequency of light from a laser. Is any any easier to calibrate a Newton meter than an Ammeter?

16. Jan 10, 2006

### rcgldr

Note I was trying to define what an amp means, not provide a method to measure current. Defining an amp in terms of electrons or Coulombs seems a lot simpler than decribing a method to measure current via the electrical field generated between two very long wires.

I'm also under the impression that if I have 1 amp of currrent in a typical wire, that at any cross section of that wire there will be net flow of 6.25 x 10^18 electrons / second across that section, unless there are magical electrons that don't have a standard amount of charge in typical wire.

17. Jan 10, 2006

### ZapperZ

Staff Emeritus
There's a difference between "equivalent" and "equal". 1 amp is equivalent to having x many electrons flowing through a cross-sectional area in 1 sec. But 1 amp is NOT equal to x many electrons per second. That is just not right dimensionally since x electrons/s is number/second, where as an ampere is coulombs/second. You were trying to indicate that those two are identical. They are not, and cause quite a confusion to anyone just learning the subject matter.

Zz.

18. Jan 10, 2006

### rcgldr

I understand your point now. You want it to be clear that 1 Amp is related to the charge, and not the mass of the electrons that I mentioned in my definition.

19. Jan 10, 2006

### rbj

but, Z, they could define 1 amp to be equivalent to having x many elementary charges flowing through a cross-sectional area in 1 sec. and that would be dimensionally the same. but it would change the definition.

an amp is not quite equivalent to having some x number of elementary charges pass some cross-sectional boundary in 1 second since we do not know (vis-a-vis the present definition of the unit of charge) exactly what the elementary charge is. now the big guys at NIST or whatever international standards body could redefine the unit charge to be the sum of a certain exact number of elementary charges, but then, as a result, $\mu_0$ would no longer be exactly $4 \pi \times 10^{-7}$ as it is in SI units.

another way of wording what an ampere is (in the present definition) is whatever current it has to be to define $\mu_0 \equiv 4 \pi \times 10^{-7}$ H/m. sorta like the meter is presently defined to be whatever length it has to be to define c = 299792458 m/s.

it's like redefining Advogadro's Number, NA to be exactly 6.023 x 1023, but that would not be the same definition as the number of Carbon-12 atoms needed to weigh precisely 12 grams.

so which universal constant do you want to define exactly by use of the definition of the unit charge (or unit current)? $\mu_0$ or e?

Last edited: Jan 10, 2006
20. Jan 11, 2006

### rbj

i didn't check the web site, but fundamentally, the Ampere was never defined as a Coulomb per second. The Ampere was defined first as whatever current it had to be to result in $\mu_0$ being exactly $4 \pi \times 10^{-7}$, or whatever current it had to be to result in 2 x 10-7 N/m force in two infinitely long parallel wires spaced apart by 1 meter. Then the Coulomb was defined to be whatever charge passes a cross-section boundary of a wire carrying 1 ampere in the time of one second. that is, the Coulomb is an Ampere-second, where the Ampere has a primary definition.

of course, it would be circular to define the Coulomb to be an Ampere-second at the same time as defining the Ampere to be the current of a rate of 1 Coulomb of charge per second.

Last edited: Jan 11, 2006
21. Jan 11, 2006

### rcgldr

Not only that web site, but also in a college text book, University Physics by Sears and Zemansky (at least in the old edition I still have). Remember the point here was a laymans definition of an ampere, other than the one quoted which referenced the two long wires.

Last edited: Jan 11, 2006
22. Jan 11, 2006

### Galileo

That's exactly the point I was making in my earlier post. The ampere is used to define the Coulomb.

23. Jan 11, 2006

### rcgldr

As previously posted, some college text books define Coulomb first, since this allows charge to be defined. Then Ampere is defined later, as a rate of charge flow per second. It's a more logical introduction into the physics of electronics, define charge first, then current and voltage.

And why ignore the web site but still include it in a quote?

24. Jan 11, 2006

### ZapperZ

Staff Emeritus
"Could" and "is" are two entirely different things. I'm not teaching history here. What is THE definition of an Ampere NOW?

Zz.

25. Jan 11, 2006

### rbj

i was just quoting you. i looked at the web site which is nice, but it is not the authority, whereas the NIST site (below) is the authority on these definitions. Layman's definitions are fine to the point that we do not tell a lie in such a definition.

Well, for the purposes of a layman, it is okay, i guess to think of the unit charge as being defined first and then to define current as the time rate of change or movement of charge. But that leaves how to define the unit charge and the answer would be the same. A coulomb of charge is such an amount of charge so that the permeability of free space $\mu_0$ come out to be exactly $4 \pi \times 10^{-7}$ Henries per meter.
you're right, Z, but sometimes these definitions get changed as the leaders in the community of physical sciences decide what is more important to have defined and what is best left as measured. but sometimes it's good to toss in a little history and i would really recommend the OP and Jeff and anyone else interested to look at the NIST site:
http://physics.nist.gov/cuu/
and particularly
http://physics.nist.gov/cuu/Units/current.html .
For example between 1889 and 1960, the hard definition of the meter was the distance bewteen the centers of two scratch marks on a piece of iridium and the second was 1/86400 of a "day", but with changes in 1960, 1967, and 1983, the definitions of the meter and second were updated in such a way as to define the speed of light in vacuum to be exactly 299792458 m/s. so now, the distances between those two scratch marks are measured not defined and comes out to be very, very close to 1 meter. and the effect on the length of day has been more noticable, given the hard definition of a second, now once in a while they have to insert leap seconds (the minute immediately before midnight 01/01/06 GMT or UTC had 61 seconds in it instead of 60) because the rotation of the earth is very gradually slowing down.
Some day (I hope soon) they will redefined the kilogram so that it is not the mass of that prototype in Paris but will be such a mass as to make Planck's Constant $\hbar$ an exact and defined number. This is essentially how the Ampere (and by extension, the Coulomb) have been defined. They are whatever they have to be so that the permeability of free space $\mu_0$ come out to be exactly $4 \pi \times 10^{-7}$ in SI units. But someday, they might very well redefine the Coulomb to be some exact defined number of elementary charges so that the elementary charge comes out to be exactly 1.60217653*x*10-19 C. But that is not the case now, so that number is measured and there is some range of error in that measurement.

Last edited: Jan 11, 2006