Electric Field Lines intersection I have been taught that Electric Lines of Force do not Intersect each other except at charges.
But then I came across this simulation: www.falstad.com/vector3de

While drawing Field lines in 2D we show no field lines in this plane but technically, field is zero only at the null point exactly at the centre if we consider equal positive charges.
Does that mean that there can be field in regions where there are no field lines?
and can Field lines intersect as shown in the image.
On thinking about this I came to a conclusion that since field is zero at null point it can have any possible direction like a zero vector so we can say field lines intersect there.
But isn't this a vacuous logic as representing directions for zero vector is meaningless.
I understand that field lines are just a representation,a human construct, but do we  consider the lines shown in the image, is there some definite rule to avoid this confusion.
One more thing I was told that Equipotential lines too don't intersect because then field would have multiple directions but then in this case, it seems as if it can .
Direction of zero field is meaningless and we don't draw Equipotential lines inside a metal as the entire conductor is equipotential, it would be ambiguous.
So Is there any standard rules we follow to draw field lines such that they don't intersect at points where there is ambiguity?
 A: On a carefully constructed sketch in three dimensions, field lines start (or end) at charges, and the line density is proportional to the field strength. This is not true for a 2D cut through a 3D sketch. In the sketch you provide, the lines should disappear as they approach the null point.
A: First of all, I'm a student new for physics so my answer ,rather precise saying opinion ;can be an incorrect perception.yet i out of pleasure  and curiosity would answer this... first of all we should understand that field lines are mere a representation of the the field strength. Field strength is actually found through the equation (F=q^2/4π€r^,2) where as field lines give us an interpretation of how strong  the field there is. If field lines are closer to each other then the strength is higher. if field lines are far from each other then the strength is lower .if there are no field lines then the strength is 0 which is a null point. Note that I used the word lines not line which means to get a certain explanation we need to have at least two or more field lines. So consider that there is a point in which it has a + charge (test charge). If you draw field lines from here then the reality would be the lines been drawn in all dimensions and directions but on the paper we only draw the 2D sketch not the reality. Since the charge is a point in space and  when the field lines are drawn ,it can be like all lines coming to one place , which is not true , but it is that the field created there is infinite :not that they cancel off( that is why I said that we should highly understand the nature of field lines are representation of strength  of field relatively). When the field lines proceed throughout the space the the space between lines increases and it means field strength decreases thereby. At a null point( has to be created by more than one charge) the the field is zero so no lines do meet that area.
Though it is said that lines do not intersect we should remember that this is said to a field that is electrostatic (charges do not move)..because when in a field where ,when the field is created due to electromagnetism(  in a  moving magnetic field ,if there are charges, according to Faraday's law there is EMF induced and it leads to a  electric Field to be created ( E=dV/dt)and that lines of field are drawn in closed circles( that is complete opposite taught in electrostatic field lines as they never appear in closed lines).so here obviously thhe line do intersect itself by which it means that non intersection can be applied only in electrostatic field.
I hope this helped.. also I'm  quite new to the app. so might do wrong things unknowingly ..please correct me if there any)
