B -H Curve or Magnetization Curve

B -H Curve or Magnetization Curve

AU: May-10, Dec.-10

• We have already seen that magnetic field strength H is NI/l. As current in coil changes, magnetic field strength also changes. Due to this flux produced and hence the flux density also changes. So there exists a particular relationship between B and H for a material which can be shown on the graph.

Key Point : The graph between the flux density (B) and the magnetic field strength (H) for the magnetic material is called as its magnetization curve or B-H curve.

• Let us obtain the B-H curve experimentally for a magnetic material. The arrangement required is shown in the Fig. 1.15.1.

• The ring specimen as a mean length of 'l metres with a cross-sectional area of 'a' square metres. Coil is wound for 'N' turns carrying a current 'l' which can be varied by changing the variable resistance 'R' connected in series. Ammeter is connected to measure the current. For measurement of flux produced, fluxmeter can be used which is not shown in the Fig. 1.15.1.

• So H can be calculated as NI/l while B can be calculated as ϕ/a for various values of current and plotted.   With the help of resistance R, I can be changed from zero to maximum possible value.

The B-H curve takes the following form, as shown in the Fig. 1.15.2.

The graph can be analysed as below :

i) Initial portion : Near the origin for low values of 'H', the flux density does not increase rapidly. This is represented by curve OA. The point A is called as instep.

ii) Middle portion : In this portion as 'H' increases, the flux density B increases rapidly. This is almost straight line curve. At point 'C' it starts bending again. The point 'C' where this portion bends is called as knee point.                                     

iii) Saturation portion : After the knee point, rate of increase in 'B' reduces drastically. Finally the curve becomes parallel to 'X' axis indicating that any increase in 'H' hereafter is not going to cause any change in 'B'. The ring is said to be saturated and region as saturation region.                                                         We have seen already that according to molecular theory of magnetism, when all molecular magnets align themselves in the same direction due to application of H, saturation occurs.

Such curves are also called saturation curves.

1. B-H Curve and Permeability

 From B-H curve, a curve of relative permeability up and H can also be obtained.

As B = µ H = µ_r µ₀ H

ஃ µ_r = B/ µ₀ H

µ₀ is constant which is 4πx10^-7. So B/H is nothing but slope of B-H curve.

Key Point : So slope of B-H curve at various points decide the value of relative permeability at that point.

• Initially the slope is low so value of µ_r is also low. At knee point, the value of slope of B-H curve is maximum and hence µ_r is maximum. But in saturation region the value of µ_r maximum and hence µ_r is maximum. But in saturation region the value of ur falls down to very low value as slope of B-H curve in saturation region is almost zero.

• The curve of us against H is shown in the Fig. 1.15.3 for a magnetic material.

• The value of µ_r  is 1 which is constant in case of non magnetic material. The slope of B-H curve is constant i.e. it is a straight line passing through the origin as shown in the Fig. 1.15.4.

2. Practical use of B-H Curves

 • While designing the magnetic circuits, magnetization curves are useful to design the values of B corresponding to H. From this, proper material with required relative permeability can be selected.

• The various materials like iron, steel are generally represented by the B-H curves and µ_r -H curves.

Review Questions

1. Draw the B-H curve and discuss in detail the B-H relationship. AU : May-10, Dec.-10, Marks 8

2. Explain the practical use of B-H curve.