# Concept of Magnetization or Saturation Curve: B-H Curve

Magnetization curve or saturation curve is basically the graphical relationship between the magnetic flux density B and magnetic filed intensity H for a given magnetic material. As we know that,

B = μ_{0}μ_{r}H

where μ_{0 }= Permeability of free space = 4πx10^{-7}Tm/A

μ_{r }= Relative Permeability of material

Thus by using the above equation, we can find the relative permeability of the material. Unfortunately relative permeability do not remain constant for a given material rather it varies with the value of magnetic flux density B and magnetic field intensity H. This variation in the value of relative permeability μ_{r} is due to saturation of the material which can be better understood by domain theory. However we will concentrate here on the magnetization curve / saturation curve.

Figure below shows a typical B-H curve for a ferromagnetic material. As can be seen from the figure below, it consists of three zones i.e. OA, AC and beyond point C. This B-H curve is known as magnetization curve / saturation curve

Initial zone OA is non linear while the zone AC is linear and beyond point C, it is again non linear. This non linear zone beyond point C is called Saturation region. It shall be noted here that tough OA is also non linear but in this zone the rate of change of B with respect to increase in H is increasing which means that increasing the value of H increases the magnetic flux density B rapidly (How am I saying this? Just draw tangent at different points between OA. You will notice that slope of tangent is increasing). But thing is not so in Saturation Region. In saturation region, the rate of increase of B with respect to increase in H is decreasing (Just draw tangent at different point beyond C. You will notice that slope of tangent is decreasing) which simply means that flux density B in the Saturation Region increases less rapidly with H as compared to its change in linear zone AC.

It shall also be noticed that in saturation region,

Relative permeability μ_{r}= B/ μ_{0}H = (1/ μ_{0})xSlope

Therefore relative permeability decreases in saturation region as the slope of curve is decreasing. Thus during magnetic circuit calculations, the value of μ_{r }and H should correspond to the flux density under consideration. For free space or non magnetic material as μ_{0 }is constant, hence magnetization curve shall be a straight line (B = μ_{0}H).

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From economic consideration, the design of rotating electrical machines and Transformer are based on the flux density somewhere in the saturation region. Therefore for analysis of magnetic circuit of electrical machinery or transformer, real B-H curve of the material used shall be considered.