# Does it really make sense to talk about field lines?

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?

• 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. – dmckee --- ex-moderator kitten Apr 9 '14 at 15:24