Warning: Layman question. Treat me as a 10 years old child
The question was based on this page.
I could write this on the physics channel, but despite the context, my problem is intrinsically related to math.
First, let's point out the context
- There are two kinds of charge, positive and negative
- Like charges repel, unlike charges attract
To calculate the charge of one object we must consider that, the more charged the more the attraction or repulsion between this object and a second referential object will exist.
Considering the two objects at a distance $d$. Both attracting each other. One force, $F_1$, will be noticed.
If we want to know and create an unity to calculate the physical quantity related to the charge of the first object, we'll need a third auxiliary object.
What we will do is compare the force $F_1$ between the object 1 and 3. Then, compare the force $F_2$ between the object 2 and 3.
So we will put the object 1 at a distance $d$ from the object 3 and calculate the exerted force.
Then we will put the object 2 at a distance $d$ from the object 3 and calculate the exerted force.
If both forces are equal, then both charges (object 1 and 2) are also equal.
But if the object 2 have a charge grater then the object 1, we need to find out the difference.
Now the math problem
How intuitively think about this problem?
So far I understand that we must consider the multiplicity, in other words, the object 2 will have
$F_2 = n.F_1$
Reading a physics book they come out with the following:
If both charges are equal then:
$\frac{a}{b} = c$
If the charge 2 are grater then the 1, then:
$\frac{a_1}{b_1} = \frac{a_2}{b_2} = ... = \frac{a_n}{b_n} = K$
Now the math layman question
I can't understand why they represent the multiplicity ($a = n.b$) in that way:
$\frac{a_1}{b_1} = \frac{a_2}{b_2} = ... = \frac{a_n}{b_n} = K$
My questions is: What is the $a_1$, $a_2$, ..., $a_n$?
Is $a$ related to the object 1 and $b$ related to the object 2 (with grater charge)?
In this case, we divided the lower value by the larger one?
Why each part are equal and finally equal to $K$ ? $\frac{a_1}{b_1} = \frac{a_2}{b_2} = ... = \frac{a_n}{b_n} = K$
Where is the third object represented?
What is $K$ ?
Looking for an intuitive concept
I'm looking for purely intuitive concept about that. To understand my question type, please read that one:
The logic behind the rule of three on this calculation
Try to use simple concepts like take as base only on multiplicity and division. At least I think it is sufficient to point out this operation. (Sorry about my leak of understanding)
I would start with something like:
If one value is $x$ times grater the $y$ and we divided $\frac{x}{y}$ we will get that common value between the two variables and then will be possible determine the multiplicity.
We have $\frac{a_1}{b_1} = \frac{a_2}{b_2} = ... = \frac{a_n}{b_n} = K$ because we are considering more then the two mentioned objects(??) ...