Question: What is the difference between magnetic flux, magnetic flux density and magnetic flux linkage? How would you define magnetic flux without just quoting a formula?

James M Monk answered on 14 Jun 2011:

The magnetic flux density is really a measure of the strength of a magnetic field along a particular direction at a particular point. The direction part is important because if you measure the flux density perpendicular to the magnetic field then the flux density is zero in that direction (even though the magnetic field is not).

You can think of this as having a surface through which the magnetic field lines pass. If the surface is parallel to the field then there is no magnetic flux passing through the surface. On the other hand, if the surface is perpendicular to the field then there is magnetic flux passing through the surface. So the flux density is the strength of the field in the direction perpendicular to the surface, while the flux is that density multiplied by the area of the surface.

Flux linkage is used in electromagnets where you can have several coils wound over each other, so the effective area of the coil is larger because there is more than one.