# Does greater number of lines of force around the magnet imply greater magnetic field strength around it?

If we sprinkle iron fillings on a sheet of glass placed over a short bar magnet. The arrangement of iron fillings will be similar to the one shown above.

Why do some of the iron fillings arrange in a particular pattern when sprinkled around a magnet, instead of getting attached to the magnet?
All the filings are resting on a surface where there is friction. If the force due to the magnet does not exceed this friction, the filings won't accelerate to the magnet (only the closest ones experiencing the largest forces do). Iron is also ferromagnetic, which means it can concentrate magnetic fields. So filings that are too far to be affected by the magnet itself can be attracted to adjacent filings which are concentrating the magnetic field better. This is why most of the filings seem to be more attracted to each other than the magnet itself. But essentially all the magnetic field is caused by the magnet.

After this good answer by gregsan to the above question, I got a doubt here. Considering gregsan reason to be true, for gaps between the fillings around the magnet. I thought, if the reason for gaps in between the fillings is due greater field strength at those gaps (caused by displacement of fillings towards the magnet), and if the reason for those lines in between the gaps is due to lesser magnetic field at those locations (causing the fillings to remain at those same position). I thought iron fillings lines around the magnet exist if magnet can't exert more force to accelerate them against the frictional force, on the other hand in the gaps, fillings are more accelerated towards the magnet, so they get attached to the magnet causing gaps. Now, I assumed the lines around the magnet to be the locations where force due to magnet is less. So, if more is the lines around the magnet, greater will be locations where force due to magnet is less. Considering this, I thought, greater number of lines of force indicate less intensity of magnetic field around the magnet, but I have been taught in my school that, field strength to be more if greater is the lines of force around the magnet. Is it that magnetic field strength will be concentrated more at a shorter distance, if lines of force is more? I don't know whether I have misunderstood the answer of gregsan or is there any reason which would account for greater number of lines around the powerful magnet? If any is the case, please explain.

• First, it's less confusing to say "question" instead of "doubt". Second, a vector field simply attaches a set of numbers $\mathbf{v} = (v_x, v_y, v_z)$ to every point in space. Drawing them as "lines" is done by imagining curves $\mathbf{x}(\lambda)$ passing through every point that have tangent vectors $\frac{d\mathbf{x}}{d \lambda}$ equal to $\mathbf{v}$. The reason we can do this to begin with is because this vector field has 3 components, and space is 3 dimensional. You can't do it if $\mathbf{B}$ had say, 7 components. Commented Dec 19, 2013 at 20:05
• The statement that the curves don't intersect is because $div(\mathbf{B}) = \boldsymbol{\nabla} \cdot \mathbf{B} = 0$, i.e., there are no magnetic monopoles, or Gauss' law. The field lines of an electric charge intersect (or at least, converge) precisely where the charge is. Commented Dec 19, 2013 at 20:06