Electric field line density : Theory vs Reality

Question

I've already went through this post. Yet, I still can't understand the meaning of "density" of electric field lines whose number is, in reality, infinite.

One of the answers , for instance, states that the ratio of two densities is independent of the number of field lines, so even when their number is infinite, they would always end up canceling each other when computing the ratio of two densities ( for the field lines generated by a point charge), the mathematical proof of this statement makes sense. However, in reality, the number of field lines is infinite, and field lines don't cancel each other, so even if we get further from our point charge, the number of field lines per unit area would still be infinite, no matter how far or near we're from the source.

Am I missing something?

Answer 1

Using the electric field line density to determine the strength of the field is a choice you make when you draw an electric field diagram. Therefore in reality there isn't an infinite number of field lines, rather there are infinitely many field lines you could draw.

This is similar to drawing lines of longitude and latitude on a globe, or grid lines on a coordinate system. There are an infinite number of coordinate lines you could draw, but to be useful you only draw a select few.

You really should just focus on the electric field. At each point in space you assign a vector that is the electric field vector. And you are good to go. You have your function $\mathbf E(x,y,z)$, and if you want to find a nice way to visualize it then you make a field love diagram where the density of lines (scale subjectively chosen by you) represents the strength of the field at that point.

Answer 2

Field line is an artistic concept. It is about visualisation. It is not a physical concept.

Answer 3

Even though it is infinite, you can not draw infinite lines on the paper. So, the density is better defined as the number of visible lines (that are finite) that passes through a given area (for example, a 1cm by 1cm square).

In places far from the source, there would be less lines passing inside the square than a place very close to the source.

Answer 4

The primary concept you are looking for is flux density, which is equivalent to the field strength. The flux of the field is well defined without infinities. The density of a finite number of field lines on a diagram gives you a little bit of information about this quantity. This information is still useful even though it is not complete. It is like how a diagram with a finite number of field lines gives you a little bit of information about the direction of the field, but you still need to extrapolate in the regions where a field line is not drawn.

The reason the field lines can tell you about flux and thus the field strength at all, is because the field lines obey a kind of 'trivial' Gauss's law, where in any gaussian surface which doesn't enclose a charge the sum of lines entering and leaving is equal to zero. The intersections by field lines work exactly like the flux itself, and so we can get some information about flux density through a diagram with a finite number of field lines.