I've just started my highschool, only to land in the beautiful world of electricity and magnetism, I have many queries and dilemmas, so I want some guidance. Now on to the question.
I've just read that the unit of charge is the coulomb, and that $1\:\mathrm{C} = 6.25 \times 10^{18}$ electrons, because charge on one electron is $e = 1.602 × 10^{-19}$ "C" . This confuses me as – if the amount of charge is the number of electrons then what is the meaning of – amount of charge on one electron? Why in coulombs?
My possible theory is that since charge is the property of matter to interact with electromagnetic FORCES, the real definition of charge should be based on how much force with which it interacts. However, wherever I se the definition of the coulomb, I always get it in amperes and the number of electrons.
Can anyone tell the difference between = number-of-electrons- Coulomb and the formula definition {for example , since Speed = Distance/Time , so, 1 km/sec = 1 km covered in 1 second. (this type) }?
EDIT – In a textbook I found it is given that – "1 coulomb is that quantity of electric charge which exerts a force of $9×10^9$ on an equal charge placed at a distance of 1 m from it. So now I want to know how this particular number is reached if it is correct?
Best Answer
I asked about this in the comments, but I will go ahead and put this as an answer.
From wikipedia:
From this we can get the definition of the coulomb. It is just the amount of charge that is transported by a $1A$ current in $1s$.
Of course how we define the charge of an electron is arbitrary. We could define a new charge unit to be the amount of charge an electron carries, or the amount of charge $10.2$ electrons carry. We would just have to adjust other units accordingly (for example, if we calculated a force we would either have to define a new force unit as well, or we would need to include a conversion in any formulas involving force to keep our forces in Newtons).
But how do we determine the charge of the electron (in nay units) in the first place? There are multiple ways, but one that is historically well known is the oil drop experiment. I won't go into the details of the experiment, you can look into that on your own, but essentially what was found is that oil drops with small amounts of charge had charges equal to integer multiples of some value of charge. It is this charge value that is the charge amount of the electron you have listed.
To go along with your edited question. The magnitude of the coulomb force between two charges of $q_1$ and $q_2$ separated a distance $r$ is given by $$F=\frac{kq_1q_2}{r^2}$$ where $k=9*10^9 \frac{N\cdot m^2}{C^2}$
If $r=1m$ and each charge is $q_1=q_2=1C$, then the resulting force is $$F=\frac{(9*10^9 \frac{N \cdot m^2}{C^2})(1C)(1C)}{(1m)^2}=9*10^9N$$