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?

  • $\begingroup$ So saying a coulomb is the amount of charge transported by $1 A$ current in $1 s$ is not sufficient? $\endgroup$ – Aaron Stevens Jul 23 '18 at 13:55
  • $\begingroup$ @Aaron Stevens plz explain why 1e = 1.6 × 10^-19 C ? $\endgroup$ – DEEKSHANT Jul 23 '18 at 14:04

I asked about this in the comments, but I will go ahead and put this as an answer.

From wikipedia:

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per meter of length

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 $$F=\frac{(9*10^9 \frac{N \cdot m^2}{C^2})(1C)(1C)}{(1m)^2}=9*10^9N$$

  • $\begingroup$ In a textbook I found it is stated that - " 1 coulomb is that quantity of electric charge which exerts a force of 9 ×10^9 newtons on an equal charge placed at a distance of 1 m from it ". And from this definition we can easily understand and calculate the charge of an electron. And also we can come to the conclusion that to reach this number almost 6 × 10^18 electrons are required. Is this correct ? Any thoughts ? $\endgroup$ – DEEKSHANT Jul 23 '18 at 15:07
  • $\begingroup$ @DEEKSHANT yes this is also correct $\endgroup$ – Aaron Stevens Jul 23 '18 at 15:36

Well, unit of charge was defined when people did not know about the electrons and protons. Electric charge back in those days was believed to be a continuous quantity.

In the CGS system electric charge is defined using force that two objects of equivalent charge apply to each other in a distance of 1cm, which is more sensible if you are just starting with electrostatics. You can find the definition of electric charge in this Wikipedia article.

By the way, the charge of an electron is not the smallest amount of charge in nature. You can have 1/3 electron charge on subatomic particles.

  • 1
    $\begingroup$ However, quarks only occur in such combinations that the charge is an integer number of electron charges. $\endgroup$ – my2cts Jul 23 '18 at 20:19

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