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Magnetic Flux
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 fluxφ 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 Tm2 but 1Tm2 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  
 
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