Field lines should only provide a visual representation of a field. There is a rule for their construction: take an object subject to a field, move it by d$\mathbf{r}$ and draw the direction of the force due to the field. Do it indefinitely, connect all the d$\mathbf{r}$ and get a line. A field line.

Some examples of common 'properties' of field lines:

The density of field lines is related to the strength of a field.

In plasma physics, there is an effect called flux freezing, where the number of field lines crossing a contour stays constant under topological changes of the contour.

BUT field lines do not occupy a physical position in space so we can draw how many we want?

Does it make sense, then, to talk about the number of field lines?

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    $\begingroup$ While I discourage people from talking about "field lines" because I see students confuse themselves that way, the construct can be made mathematically equivalent to a vector field that is divergenceless except at charges. So this becomes a questions about pedagogy. $\endgroup$ – dmckee --- ex-moderator kitten Apr 9 '14 at 15:24

It does make sense to talk about the number of field lines, but only if you take care to represent the field amplitude as being inversely proportional to the spacing between the lines. With that, the total number of lines crossing a surface is proportional to the flux, etc.

Some people, notably textbook authors Chabay and Sherwood, feel that the field line concept causes more problems than it solves. (They do agree that the concept is useful in plasma physics.) I don't happen to agree with them, personally.


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