final step is to put a small arrow on the line lU Il tric field at that point). We can then do this again, starting at a new point in th. generate another electric field line. If we do this from enough different st l in enough diferent directions, we can get a sample of lines throughout the reoi wn in Figure 16.11 This sounds like a complicated process-and it is. The good news is that we rn a good deal through qualitative (non-numerical) sketches of electric field lines, with ving to do any calculations. Your choice of the number of lines to draw is arbitrar ce a choice is made, the following rules should be obeyed: the region, as can often Out 1. Electric field lines never cross 2. Electric field lines begin on positive charges and end on negative charges. If the re you are considering contains more positive than negative charges, some lines will leave the region, and never return. If the region contains more negative charge, some lines will come in from outside the region. 3. The lines entering or leaving a point charge are distributed evenly around the charge One thing that is perhaps a little surprising about the sketches of electric field lines that re produced following these rules and the procedure of Figure 16.10 is that the relative rength of the electric field at each point in space turns out to be strictly proportional to how ensely packed the lines are in the region around that point. To see what this means, consider he 3-dimensional picture shown in Figure 16.12. Here, we follow four diverging field lines as hey first intersect the small circular surface A, and then the larger circular surface A,. The ize of each surface is chosen to just catch these four lines and no more. It then turns out that he electric field in the region near each of the surfaces is exactly proportional to the density of field lines intersecting the surface. Once we have decided how many field lines to draw to epresent the field due to a particular charge, the proportionality may be writtern Eo number of field lines crossing a surface 16.7) area of the surface Equation 16.7 says only that the electric field is proportional to this density of e numerical value of the electric field directly from the field lines In fact, the number of feld lines we drew was our own arbitrary choice. Nevertheless.t ld ketches are useful for understanding a lot of qualitative things about the elect the future, we just need to remember that: first, the ele ric ctric field at ngent to the field line passing through that point; second, the strength of the electric field is prop or tional to the density of electric field lines, as in Equation 16.7; and third, for a poil at th