Question

How do magnetic flux and magnetic fields relate to magnetic field lines?

Answer 1

Value of the magnetic flux through a given area is equivalent to the number of magnetic field lines passing through that surface area. So if an area is represented with densely packed magnetic field lines in its vicinity then we can infer that the value of magnetic flux is high at that point in space and vice versa.

So when we see a typical picture of magnetic lines around a bar magnet, one can notice dense lines around the poles and sporadic field lines in the regions away from the magnet. Thus we can say that magnetic flux near poles is significantly higher than that at any other place around bar magnet.

Now, lets write the relationship between magnetic field and magnetic flux in mathematical formula:

magnetic field (also called magnetic flux density) B is related to magnetic flux 'phi' as:

here, A is the surface area.

Thus we can see from above relation that magnetic field is equal to the magnetic flux (in turn, magnetic field lines) passing per unit area.