The principle of conservation of electric charge (or law of conservation of electric charge)
affirms that:
in a closed (isolated) system, which does not exchange any matter with the outside, the algebraic sum of all the positive and negative charges and negative charges in it remains unchanged in the time.
It represents a postulate of the physics.
We suppose that I have an isolated system with this drawing where there are three charges $q_1, q_2$ and $q_3$ with $q_2$ have positive sign where I know the value. In addendum I know $r_{12}$ and $r_{23}$; hence the $r_{12}+r_{23}=r_{13}$:
I know that the system is isolated and therefore named the $F$ the generic coulombian forces:
$$\sum_{\forall \, \text{coulombian force}} F =0.$$
Equivalentely:
\begin{cases}
\dfrac{k_0|q_1q_2|}{r_{12}^2} =\dfrac{k_0|q_2q_3|}{r_{23}^2} \\
\dfrac{k_0|q_1q_2|}{r_{12}^2} =\dfrac{k_0|q_1q_3|}{r_{13}^2}\, \text{ or }\, \dfrac{k_0|q_2q_3|}{r_{23}^2} =\dfrac{k_0|q_1q_3|}{r_{13}^2}\\
\end{cases}
Now I will find the values of $q_1$ and $q_3$ knowing $q_2$.
My question is:
If I have many charges in an isolated system is it possible to have this condition?
$$\sum_{i=1}^N q_i=0 \tag 1$$
i.e. exist this condition?
Is it possible to apply in general the $(1)$ in the case of my drawing?
Best Answer
There is no law $$\sum q_i=0$$ if the system is closed its true that $$\sum q_i=Q=\text{ const.} $$
In your task somebody just put the three charges at his will.