The strength of a magnetic field is characterized by by a quantity called
the magnetic flux density. 

The idea probably comes from the fact that, on diagrams showing magnetic
field lines, regions of stronger magnetic field have a greater concentration
of lines (ie a greater density of lines). 

In many situations we find that something more equivalent to total quantity
of magnetic field seems to be important. 



For this reason we now define the quantity, magnetic flux, φ as follows 



In words: 

If an area A is at 90° to a magnetic field of flux density B then the
flux threading (or flux linking) that area is given by the
product of the flux density and the area. 



The units of flux are therefore Tm^{2} but
1Tm^{2} is called
1Weber (1Wb) after German physicist
Wilhelm Weber. 



If the area being considered is not at 90° to the flux lines
(as shown in the next diagram) we
define the flux linking it by using the component of the flux density which
is at 90° to the area. 



The magnitude of the component of B which
is perpendicular to the plane of the area here is 



Notice that the angle θ is not the angle between the plane of the area
and the flux lines but the angle between a normal to the plane of the coil
and the flux lines. 

Therefore, in this case, the flux threading or linking this area is defined
to be 



If the area in question is the area of a coil of wire having N turns, (which
it frequently is, in practice) then we now define the flux linkage
of the coil as 


