So, I've been reading an introductory book to physics. I've gotten to the point where I understand Coulomb's law, and now the book is introducing electric fields.
I'm having a hard time understanding why that unit is useful, and how to apply it to charges. (Force per Coulomb)
Here's a "practical" example...
Supposing the dielectric between two charges is air, $q_1$ is a hydride anion, $q_2$ is a hydrogen cation, and the ions are 1 μm apart.
$k = 9 * 10^9Nm^2/C^2$
$q_1 = -1.6 * 10^{-19}C$
$q_2 = 1.6 * 10^{-19}C$
$r = 1μm$
Using Coulomb's Law we can get the force $f$ in newtons:
$$\frac{kq_1q_2}{r^2}$$
$$\frac{(9 * 10^9Nm^2/C^2)(1.6 * 10^{-19}C)(1.6 * 10^{-19}C)}{(1*10^{-6}m)^2}$$
Barring any errors, this works out to $2.304*10^{-16}N$
The equation for an electric field is:
$$E=\frac{F}{q}$$
This unit looks remarkably similar to weight. (Another unit that seems useless and arbitrary to me.)
My book says that knowing an electric field, we can get the force on any charge within it. I would assume that would be done using Algebra and getting:
$$F=qE$$
I understand how one might get $E$ for a single charge. (I.E. one of the ions) But, the book also says electric fields are applicable for more than one charge, yet shows no example of that.
I'm at a loss as to what I would plugin for the variables to get the electric field in my practical example.
In addition, I don't understand how this proportion would be maintained without distance.