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I´m currently studying electrostatics and I´m having a hard time understanding why do the number of electric field lines is proportional to the intensity of electric field? I just don´t see it.

Can we formally derive a formula that relates the number of electric field lines $N$ and the intensity of the electric field $|\vec E|$?

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  • $\begingroup$ No. The number of field lines is not countable. Maybe you are confused about the concept of "flux"? $\endgroup$ – nabla Dec 29 '15 at 1:46
  • $\begingroup$ In resnick vol 2, in the section of electric field, it says that the intensity is proportional to the number of field lines and the perpendicular area; but it doesn´t formally explain it $\endgroup$ – user128422 Dec 29 '15 at 1:56
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    $\begingroup$ Field lines are just a neat model to use when discussing fields, and by convention, the closer the field lines, the greater the E strength. $\endgroup$ – lightweaver Dec 29 '15 at 1:59
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    $\begingroup$ @lightweaver that is the answer, not a comment... $\endgroup$ – Floris Dec 29 '15 at 2:15
  • $\begingroup$ Shade the closer lines dark to light on the outer lines. $\endgroup$ – Muze the good Troll. Dec 29 '15 at 2:38
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Field lines are just something we use to visualize the direction of the electric field vector. It's a standard convention to draw them so that the density of the lines is proportional to the strength of the field. It's not a fact of nature, it's part of the definition of how you draw the lines.

If you have a system with a small number of point charges, then this convention becomes an analogy to Gauss' Law

$$\nabla{}\cdot\vec{E} = \frac{\rho}{\varepsilon_0}$$

In terms of field lines, this basically becomes the rule that field lines can only begin or end on a charge.

If you follow this rule and draw the field lines uniformly exiting or entering each charge, then you will naturally end up with the density of field lines proportional to the strength of the field.

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