# Number of electric field lines and intensity of electric field

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 $|\vec E|$?

• No. The number of field lines is not countable. Maybe you are confused about the concept of "flux"? – nabla Dec 29 '15 at 1:46
• 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 – user128422 Dec 29 '15 at 1:56
• 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. – lightweaver Dec 29 '15 at 1:59
• @lightweaver that is the answer, not a comment... – Floris Dec 29 '15 at 2:15
• Shade the closer lines dark to light on the outer lines. – Muze the good Troll. Dec 29 '15 at 2:38

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