Why is the basic charge not equal to the reciprocal of a Coulomb?

In summary, the number of e or p constituting a Coulomb is not equal to the reciprocal of the 'basic' charge.
  • #1
snowjoe
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0
why isn't the number of e or p making a Coulomb the same as the reciprocal of the 'basic' charge if the basic charge is defined as a fraction of a Coulomb?

basic charge = 1.6 x e-19C, but number of p or e constituting a C is 6.25 x e18
 
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  • #2
Yes? 1/1.6e-19 = 6.25e18
 
  • #3
Orodruin said:
Yes? 1/1.6e-19 = 6.25e18
thank you. i may be getting stupid, but why isn't the number of e or p 1.6 e19, if each e or p, basic charge, has a charge
Orodruin said:
Yes? 1/1.6e-19 = 6.25e18


there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?
 
  • #4
snowjoe said:
thank you. i may be getting stupid, but why isn't the number of e or p 1.6 e19, if each e or p, basic charge, has a charge
Because 1/1.6 is not equal to 1.6. Imagine instead that 1 C was the charge of 20 = 2e1 protons. This would make the basic charge 1/20 = 0.05 = 5e-2 C. Obviously, this is not equal to 2e-1, which it would be if you applied the same logic as the one you just applied.

snowjoe said:
there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?
Because 10*1/10 = 1 while 1.6e19 * 1.6e-19 = 1.6^2, which is not equal to one.
 
  • #5
snowjoe said:
there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

If quantity X is 0.2 of Y, then 1/0.2 = 5, meaning it takes 5X to equal Y. If X is 15 millionths of Y, then 1/0.000015 = 66,666, so it takes 66,666 X to equal Y.
 
  • #6
Drakkith said:
If quantity X is 0.2 of Y, then 1/0.2 = 5, meaning it takes 5X to equal Y. If X is 15 millionths of Y, then 1/0.000015 = 66,666, so it takes 66,666 X to equal Y.
still, .2 is 1/5. and 5x = y so if a quantity is 1/ 15 millionth of another it would take 15 million of that quantity to equal that other, as it requires 5 of the amount that is 1/5 (.2) of another to equal that other amount
 
  • #7
snowjoe said:
so if a quantity is 1/ 15 millionth of another it would take 15 million of that quantity to equal that other

No it doesn't. I just showed you the math in my post.
 
  • #8
i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity. the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5
 
  • #9
snowjoe said:
i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity.
I have no idea what you mean here.

the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5
That's because 0.2 = (2/10) = (1/5) in its simplest terms, and 5 * (1/5) = 1.

However,
1 / 1.6 = 1 / (16 / 10) = (10 / 16) = 5 / 8 = 0.625
 
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  • #10
snowjoe said:
i know, the math makes sense, but i can't see my way around the logical demand that a fractional part of a quantity is that fraction because it takes the amount denominated to equal the whole quantity. the example of .2 follows this logic, five .2s equal the whole, .2 is the fraction 1/5

Yes, but look at your original numbers.
basic charge (c)= 1.6 x 10-19C
C = 6.25 x 1018c

1.6 x 10-19 is already a fraction equal to 1/6.25x1018, just like 0.2 is a fraction equal to 1/5. You multiply 0.2 times 5 to get 1, and you multiply 1.6x10-19 by 6.25x1018 to get 1.

snowjoe said:
there's something I'm not getting. if a quantity x was 1/10th of y, it would take 10 x's to make y. why not 1.6 e19 e or p to make 1 C?

If you're getting confused over the fact that 1.6x10-19 is not 1/1.6x1019, then the only way I know of understanding this is to just do the math.
1.6x10-19 = 1/X
1.6x10-19X = 1
X = 1/1.6x10-19
X = 6.25 x 1018

Similarly: 0.2 = 1/X
0.2X = 1
X = 1/0.2
X = 5
 
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  • #11
Let's say it takes N electrons to make up one coulomb of charge then

N x e = 1 C

so

N = 1 coulomb / 1.6 x 10-19 coulomb

Historycally the coulomb, a certain amount of charge or electrons, was defined
via the ampere - the amount of current in 2 parallel wires 1 meter apart in a vacuum
when the magnetic force on one meter of these wires is 2 x 10-7 Newton.
 
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  • #12
snowjoe said:
i know, the math makes sense, but i can't see my way around the logical demand...
Is math not logical enough?
 
  • #13
andrevdh said:
Let's say it takes N electrons to make up one coulomb of charge then

N x e = 1 C

so

N = 1 coulomb / 1.6 x 10-19 coulomb

Historycally the coulomb, a certain amount of charge or electrons, was defined
via the ampere - the amount of current in 2 parallel wires 1 meter apart in a vacuum
when the magnetic force on one meter of these wires is 2 x 10-7 Newton.

I do not think this is where the OP's confusion lies, but rather in the fact that the reciprocal of 1.6e-19 is not 1.6e19, see post #4.
 
  • #14
Yes, that is why I started to mention the definition of the ampere.
Maybe that might clear it up.
 
  • #15
Drakkith said:
Yes, but look at your original numbers.
basic charge (c)= 1.6 x 10-19C
C = 6.25 x 1018c

1.6 x 10-19 is already a fraction equal to 1/6.25x1018, just like 0.2 is a fraction equal to 1/5. You multiply 0.2 times 5 to get 1, and you multiply 1.6x10-19 by 6.25x1018 to get 1.
If you're getting confused over the fact that 1.6x10-19 is not 1/1.6x1019, then the only way I know of understanding this is to just do the math.
1.6x10-19 = 1/X
1.6x10-19X = 1
X = 1/1.6x10-19
X = 6.25 x 1018

Similarly: 0.2 = 1/X
0.2X = 1
X = 1/0.2
X = 5
Thanks, you explained this beautifully
 
  • #16
A.T. said:
Is math not logical enough?
yeh, math, logical, mind, not so much, sometimes
 
  • #17
The mind is much like a muscle.
The more you use it the stronger it gets.
 

What is basic charge?

Basic charge refers to the fundamental unit of electric charge, which is carried by particles such as electrons and protons. It is denoted by the letter "q" and is measured in coulombs (C).

What is a coulomb?

A coulomb is the unit used to measure electric charge. It is equivalent to the charge of approximately 6.241 x 10^18 protons or electrons. One coulomb of charge is also equal to the amount of charge that passes through a wire in one second when a current of one ampere is flowing.

How is charge measured?

Charge is measured in coulombs using an instrument called an electrometer. This device consists of two metal plates separated by a small gap and is able to measure the amount of charge present on the plates. The unit of charge, the coulomb, is named after the French physicist Charles-Augustin de Coulomb.

What is the difference between positive and negative charge?

Positive charge refers to the presence of more protons than electrons, while negative charge refers to the presence of more electrons than protons. Opposite charges attract each other, while like charges repel each other. The charge of an object can be determined by the number of excess or deficient electrons it contains.

How is charge transferred?

Charge can be transferred through various processes such as conduction, induction, and friction. Conduction involves the transfer of charge through direct contact between two objects. Induction occurs when a charged object is brought near an uncharged object, causing the uncharged object to become polarized and attract opposite charges. Friction involves the transfer of charge when two objects rub against each other, causing electrons to transfer from one object to the other.

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