I understand that while defining charge, Coulomb had to choose any arbitrary value of $k$ to describe unit of charge. But, why did we chose $9\cdot10^9 \rm Nm^2/C^2$ as the value of $k$, but not any other arbitrary value of $k$ like one, five, etc.? Also, please explain in full detail, I am in full confusion.
$\begingroup$
$\endgroup$
0
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
This is some ways a duplicate of Why is a second equal to the duration of exactly 9,192,631,770 periods of radiations?.
The system of units developed historically and metrologists have become better and better making readings which are reproducible and accurate as can be seen from the number of significant figures used in the definition of the second.
When something better (better reproducibility and accuracy) comes along a new definition is made to agree to the claimed accuracy of the old unit definition so as to reduce the number of measuring instruments which have to be recalibrated.
In the case of the new definition of the coulomb the constant $k$ is not exactly $9\times 10^9$ but rather $8.987 551\dots \times 10^9$ and is chosen so that ammeters etc do not have to be recalibrated for the overwhelming majority users.
Let's consider your proposal of $\dfrac {Fr^2}{q_{\rm new}^2}=\left[ \dfrac{1}{4\pi \epsilon}\right] = 1$.
This would make $1\,\rm singer$ (the new unit of charge which you are proposing) equal to $94868\dots \,\rm coulomb$ with a knock on effect on the unit of current, etc.
So you would need to recalibrate or uses conversion tables for all current instruments, textbooks etc.
And what would be the gain?
A constant which most people do not care/know about which is a nice whole number which may be superseded in the future when other measuring techniques are found to be better.
