# Quantisation of Electric Charge

Discussion in 'Physics' started by logearav, Jan 20, 2015.

1. ### logearav Thread Starter Member

Aug 19, 2011
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0
Quantisation means charge always exist in integral multiples of magnitude of charge of electron and to put it mathematically we say q = ne, where n is an integer 1,2,3,4 ... -1,-2,-3,... etc. Numerous print and web materials say that charge cannot exist in fraction or decimal, i.e, 2.3e, 4.6e etc. Agreed.
The value of e is 1.6*10^-19 C which itself contradicts the statement that no fraction or decimals is possible while dealing with charge.
Also if we take n = 2, we get q = 3.2*10^-19, n =3 means q = 4.8 *10^-19 which are all fractions.
Can experts throw light on this aspect? Thanks in advance.

2. ### ericgibbs AAC Fanatic!

Jan 29, 2010
2,606
396
hi,
This means the magnitude of charge of an electron is considered as unit charge. ie: =1

E

Nov 9, 2007
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4. ### WBahn Moderator

Mar 31, 2012
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You are confusing the notion of an integer multiple of the electronic charge (let's ignore subatomic particles) with the charge expressed in coulombs being an integer.

Let's use a simple example. You are interested in devising a unit of measure for something and you arbitrarily choose to call the amount of this substance that fills a one liter container a "charlie". Years later someone discovers that this substance is actually made up of tiny spheres that are always exactly the same size. Initial investigations indicate that somewhere between 42.5 and 42.6 billion (10^9) of these spheres are needed to make a charlie. Many years after that it is determined that 42,562,834,621 of these spheres are not quite enough to make up a charlie but that one more sphere actually comes out a bit over a charlie. It is later estimated that, it would take, to a best estimate, it would 42,562,834,621.375 to make a charlie. That fact this now has a fractional part does not mean that there are fractional spheres, just that it is impossible to make something that is exactly one charlie. And how many charlies is one of these spheres? Well, the best estimate would be

(1 charlie/42,562,834,621.375 spheres) or about 2.3494675786885e-11 charlies/sphere

Do you see how none of this has any impact on the fact that this substance is quantized?

5. ### MrAl Distinguished Member

Jun 17, 2014
2,573
523
Hi,

I have to agree with most of the other posts here. If we have something we are calling a 'unit', then we can always say we have two of them, three of them, four of them, etc., without any problem at all.
Example:
If we have a car that weighs 4000 pounds and we have a whole parking lot of 50 of these cars, then we can say with no problem that we have 50 cars. If later we find that the cars really weigh 4123 pounds, we can still say we have 50 cars. If then later we find they really have 4123.711 pounds we can STILL say we have 50 cars.
So the quantization unit can be any value even though we must always have an integer number of those things.

I can surely see the reason for asking this though, because it may seem strange that we can get a fractional value when we add up all the units. The reason for doing this is so we can better understand and deal with nature. In the above parking lot if we had to keep track of the weight we'd have to add up all the weights or at least multiply to get a total weight of 200000 pounds, but then later we'd have to do it with the more exact number and get 206150 pounds, then later yet we'd get 206185.55 pounds. Saying that we have 50 cars we dont have to do that every time it changes, and since this appears to be closer to nature anyway it makes sense.

6. ### tjohnson Active Member

Dec 23, 2014
618
122
I agree with the other posts here, but I thought an additional example might be helpful.

It's similar to the difference between the metric and English system. Suppose a person who never heard of the English system measured two boards, one a foot and the other a yard long. They might think it odd that the decimal lengths 30.48 cm and 0.9144 m were used.

A ruler or yardstick is a whole number of inches long, but a decimal number of centimeters. Likewise, electron charge is always an integral multiple of e (except for quarks, as mentioned above by studiot), but a decimal number of Coulombs.

By the way, I think the metric system is a lot better than the English one, as all physicists should.

Last edited: Jan 30, 2015
7. ### ericgibbs AAC Fanatic!

Jan 29, 2010
2,606
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Morning tj,
That should read ex-English, we went Metric in the 1970's.

During the 1950/60's, college maths using Imperial units was an absolute nightmare, thank goodness we changed over.

E

8. ### tjohnson Active Member

Dec 23, 2014
618
122
I suppose it's more accurate to call it the U.S. customary system. It's funny how the U.S. currently uses both systems. I remember reading that we buy meat by the pound, but measure the amount of fat in it grams, and we print 4"x6" photos from 35mm film. I think most American physics textbooks use SI units, which makes calculations much easier. I can never keep straight how many ounces are in a pint and pints are in a quart, but the metric system just seems to make sense for a base-10 number system.

9. ### WBahn Moderator

Mar 31, 2012
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The metric system is far superior for just about everything. There are some practical advantages to a system based on halves because it is pretty easy for someone to cut something in half or to double something without using any measuring tools and be reasonably accurate (accurate enough for what is needed at the time). Given the lack of measurement tools when the system evolved, I imagine that had a large influence on it.

The U.S. has a number of factors that have frustrated attempts to switch over including such things as a very large, diverse population coupled with a very extensive and entrenched industrial infrastructure. The same factors really hurt us as electronics went to surface mount (we already had a well-established, mature, and reliable through-hole infrastructure and so the early surface mount movement cost more than the benefits gained) and as communications went to cell phones (we already had a well-established, mature, and reliable copper infrastructure). Those put us behind the curve as countries that didn't have that were able to convert (or start almost from scratch) with the new technology. But market forces have dragged the U.S., often kicking and screaming, to the new technologies. But it's a slow process. The same is happening with the conversion to metric, but it is an even slower transition because, frankly, the switch doesn't bring much significant benefit and does present significant cost at the level where it matters -- today for the average taxpayer.

10. ### amilton542 Active Member

Nov 13, 2010
494
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Here's a thought experiment. Consider what would happen if the charge of a proton instantaneously changed to something like 1.0000001 e whilst the charge of an electron remained fixed at -e.

11. ### WBahn Moderator

Mar 31, 2012
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You'd have a lot of positive charged things being ejected to the far fringed of the universe and everything we interact with would be essentially neutrally charged but with an excess of electrons. That would change many of the chemical and physical properties of substances.

12. ### studiot AAC Fanatic!

Nov 9, 2007
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But would it make my beer fizz?

13. ### WBahn Moderator

Mar 31, 2012
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If you were in the far fringes of the universe.

Of course, it might make YOU fizz out there!

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

Sep 22, 2013
2,185
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If the charge is out of balance......a positive and negative would still join once.........but after that, everything would be repulsive.......because of net charged particles.