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This question is related for students of an high school. The that force lines can be used to represent an electric field. Lines of force have three fundamental properties:

1. Lines of force always emerge from a positive electric charge;

2. The resulting electric field is always tangent to the line of force at every point;

3. The intensity of the electric field is directly proportional to the number of lines of force passing through the unit area.

In relation to point 3., is there a physical relationship, without using Gauss's law, where the lines entering or leaving a charge is proportional to the magnitude of the charge? There are such problems in a school textbook without introduce Gauss's law.

Example: I have this image

enter image description here

Let us assume that the central charge $q_2$ is $10$ C. In this example the number of lines of force starting from $q_2$ is $16$. The lines of force coming out of $q_1$ and $q_3$ are half. So the charge on them must be $5$ C.

Addendum: I attach the screenshot of another Italian textbook in relation to point 3. without to introduce the electrostatic field flow. There is written Faraday's criterion ("criterio di Faraday"). >So is this Faraday criterion included only as a rule, or can it be proofed without the electrostatic field flow?

enter image description here

Related off-topics: Electric field lines properties and Flux received by a negative charge

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    $\begingroup$ The force lines represent the trajectory that a test charge would follow if it were placed in the vicinity of a charge generating an electric field is not true. $\endgroup$
    – Farcher
    Oct 17, 2021 at 21:54
  • $\begingroup$ @Farcher hi. Now i am improving by your comment. $\endgroup$
    – Sebastiano
    Oct 17, 2021 at 22:12
  • $\begingroup$ Is it an intuitive explanation of why "The intensity of the electric field is directly proportional to the number of lines of force passing through the unit area." is true that you are asking for? $\endgroup$
    – NeuroEng
    Oct 17, 2021 at 22:16
  • $\begingroup$ @NeuroEng no, Sorry. I not want to use Gauss law where the flux Is related with the area. $\endgroup$
    – Sebastiano
    Oct 17, 2021 at 22:19
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    $\begingroup$ Some authors may avoid mentioning point $3$, because the dimension has to be squeezed to $2$-D. Your problem shown is rather a pedagogical example. See another post of mine here and also quantitative treatment for $2$-D here. $\endgroup$
    – Ng Chung Tak
    Oct 18, 2021 at 18:30

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