The post Magnetization Curve Explanation appeared first on Electrical A2Z.
]]>A curve, or loop, plotted on BH coordinates showing how the magnetization of a ferromagnetic material varies when subjected to a periodically reversing magnetic field, is known as Hysteresis Loop or Magnetization Curve.
NonMagnetic Materials
The reluctance of nonmagnetic materials is not affected by the density of flux in those materials. Flux (Φ) therefore will vary directly with the m.m.f. (IN), and flux density (B) will consequently vary directly with the magnetizing force H.
For nonmagnetic materials, B varies directly with H and therefore the graph of B against H will be a straight line.
Magnetic Materials
When values of B are plotted against values of H for a magnetic material, the resulting graph is in the form of a curve. Table 1 shows figures for an iron sample.
Table 1 Magnetization Curve for a Magnetic Material
Magnetizing
force H (At/m) 
Flux density
B (Wb/m^{2}) 
Permeability
μ= B/H 
Relative
permeability μ_{r} = μ/μ_{o} 
100  0.04  0.00040  318 
200  0.12  0.00060  477 
300  0.40  0.00130  1058 
400  0.90  0.00225  1790 
500  1.00  0.00225  1591 
600  1.06  0.0017  1408 
700  1.11  0.00159  1265 
800  1.15  0.00144  1146 
900  1.18  0.00131  1042 
1000  1.21  0.00121  963 
1200  1.25  0.00104  828 
1400  1.29  0.00092  732 
1600  1.32  0.00083  660 
2000  1.36  0.00068  541 
A graph plotted from these figures is shown in Figure 1. Since values of B are plotted against values of H, the graph is known as a B/H curve or magnetization curve. These curves are commonly used as a means of comparing the magnetic characteristics of different types of magnetic materials.
Figure 1 Flux – magnetization curve
Magnetic Saturation
Reference to the B/H curve in Figure 1 shows that, when the value of H is low, small increases in the value of the magnetizing force (H) will produce large increases in the value of the flux density (B). This is shown by the section of the curve that slopes steeply.
For higher values of H and B, it can be seen that increases in H will produce progressively smaller increases in B. Further increases of H to the value H3 will result in an even smaller increase in B from B2 to B3. As the magnetization increases towards 2000 AT/m, the flux density increases less and less. This indicates that magnetic saturation is taking place.
Saturation is said to occur at a flux density near the center of the ‘knee’ of the B/H curve. In practice, it is not economical to magnetize steel to a flux density much beyond the point of magnetic saturation. A large increase in magnetizing current produces only a small increase in flux density, resulting in a waste of electrical power, without achieving any useful increase in flux.
The permeability of ferromagnetic materials changes with differing values of flux density. For a given flux density, permeability (μ) is equal to the ratio B/H, which may be proved by applying the basic magnetic equation in the following manner:
Table 1 gives typical values of B and H for iron. Therefore it is possible to calculate permeability for each particular flux density and magnetizing force. In Table 1 columns 3 and 4, values for μ and μ_{r} have been calculated from the given values of B and H.
The values of μ_{r} have been plotted against the values of H in Figure 1 to give the μ_{r}/H curve. The graph shows that the permeability curve rises steeply to a peak. Beyond this point of maximum permeability, the curve slopes away quite rapidly. This indicates that permeability becomes progressively less as H is increased beyond the value that causes magnetic saturation.
Figure 2 illustrates the magnetization curves for silicon steel, cast steel and cast iron.
Figure 2 Magnetization Curves
The following points should be noted:
1.  The materials tend to become magnetically saturated in the region that corresponds with the centers of the ‘knees’of the respective curves. 
2.  When the value of H is in the lower ranges, much greater flux density will be produced in silicon steel compared with cast steel or cast iron. 
3.  Silicon steel saturates at a slightly lower value of flux density than cast steel. 
4.  Cast iron saturates at much lower values of flux density than either silicon steel or cast steel. It is also much harder to magnetize than either of the above materials. 
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]]>Reluctance is comparable with resistance in an electric circuit and, like resistance, depends on a number of factors:
1.  Length of a magnetic circuit. Reluctance varies directly with the mean length of a magnetic circuit and is similar in this respect to electrical resistance:

2.  Crosssectional area of a magnetic circuit. Reluctance varies inversely with the crosssectional area of a magnetic circuit:

3.  Permeability of the circuit material. The term permeability is used as a measure of the ease with which materials may be remagnetized. Reluctance, on the other hand, is a measure of the opposition to flux. Permeability is analogous to the resistivity of an electric circuit:
where:

The total mean length of the path of an iron core is 200 mm. The core is rectangular in crosssection with dimensions 15 mm × 10 mm. If the core has a relative permeability of 830 at the designed flux density, calculate the reluctance of the core. (Remember to convert to base units.)
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]]>The permeability of a material is defined as the ease with which a flux can be created in that material. If there is no material, such as in a vacuum, the value can be shown to be 4E – 7π (or 4πE – 7; if you prefer). That is the permeability of free space (a vacuum), which has the abbreviation µ_{o}.
The permeability of free space is the reference against which the permeability of other materials is compared.
To compare the permeability of any given material with the permeability of free space, it is necessary to use a ratio µ_{r} which is known as the relative permeability of the material. For air and other nonmagnetic materials, µ_{r} has the value of unity (µ_{r} = 1).
\[{{\mu }_{r}}=\frac{\mu }{{{\mu }_{o}}}\]
If the nonmagnetic core of a solenoid is replaced with a magnetic material, the flux produced by the same number of ampereturns may be greatly increased. The ratio of the flux produced by the magnetic core to that produced by the nonmagnetic core is a direct result of the relative permeability of the magnetic material. For some magnetic materials µ_{r} can have a value in the thousands.
For any one magnetic material, the relative permeability value can vary considerably, being dependent on the flux density in the material. Relative permeability is higher at low values of flux density.
To find the absolute permeability of a material, the permeability of free space is multiplied by the relative permeability of the material:
\[\mu ={{\mu }_{o}}{{\mu }_{r}}\]
Where:
Example
Calculate the absolute permeability for a magnetic material whose μ_{r} is 800.
Solution
\[{{\mu }_{r}}=\frac{\mu }{{{\mu }_{0}}}\]
From above equation, we have
\[\mu ={{\mu }_{0}}{{\mu }_{r}}=800*4\pi *~{{10}^{7}}\]
\[\mu =3200\pi *~{{10}^{7}}~{}^{H}/{}_{m}\]
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]]>The post Magnetic Flux Density (B) appeared first on Electrical A2Z.
]]>Magnetic Flux density is the measure of the number of magnetic lines of force per unit of crosssectional area.
The general symbol for magnetic flux density is B and the unit is the weber per square meter (Wb/m^{2}). One weber per square meter is called a tesla (T).
If both the total flux and the area of the magnetic path are known, the flux density is found from:
Where:
A magnetic circuit has a crosssectional area of 100mm^{2} and a flux density of 0.01T. Calculate the total flux in the circuit.
Note: The answer is expressed in webers and not in lines of force.
An air core coil has 0.65 μ Wb of flux in its core. Calculate the flux density if the core diameter is 4 cm.
Solution
First, we’ll calculate the core area:
\[A=\pi ~{{r}^{2}}=3.14*{{\left( 0.02m \right)}^{2}}=1.256*~{{10}^{3}}~{{m}^{2}}\]
Now, we can calculate the magnetic flux density using the following formula:
\[B=\frac{\varphi }{A}=~\frac{0.65*~{{10}^{6}}~Wb}{1.256*~{{10}^{3}}~{{m}^{2}}}=5.175*~{{10}^{4}}~T\]
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]]>The post Magnetic Field Intensity appeared first on Electrical A2Z.
]]>The m.m.f. required to magnetize a unit length of a magnetic path is termed the magnetizing force or magnetic field intensity (H) for that portion of the magnetic circuit.
The magnetic field intensity is applicable only to that section of the magnetic circuit, made of the one material and with a constant crosssection. The unit is expressed in ampereturns per meter and the symbol is H.
In a similar fashion to that for magnetomotive force, the ‘turns’ part of the expression is dimensionless and in pure SI units should be omitted, leaving it as amperes per meter. For all practical purposes, however, the more descriptive term is ampereturns per meter. That is:
Where:
Note: Be sure to convert length into meters! Magnetizing force must not be confused with magnetomotive force.
Example
Find the magnetic field intensity (H) in the magnetic circuit given below:
Solution:
Here, we will calculate the magnetic field intensity (H) using the following formula:
\[H=\frac{N\times I}{l}=\frac{(2.5*{{10}^{2}})*(1.5*{{10}^{1}})}{1.2*{{10}^{1}}}\]
\[H=\frac{3.75*{{10}^{1}}}{1.2*{{10}^{1}}}=3.125*{{10}^{2}}At/m\]
If we change the dimensions of the magnetic path, the value of H would also change. For example, if we double the length of the magnetic path, we should anticipate the value of magnetic field intently (H) to decrease to onehalf its original value calculated above.
If, for the above magnetic circuit, physical dimensions are, then magnetizing force (H) will be;
\[H=\frac{3.75*{{10}^{1}}}{2.4*{{10}^{1}}}=1.5625*{{10}^{2}}At/m\]
So, we can clearly see that, for a given number of ampereturns, the magnetizing force varies inversely per unit length of the total magnetic path.
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]]>The post Magnetomotive Force (MMF) appeared first on Electrical A2Z.
]]>The force required to create a magnetic field is called the magnetomotive force, abbreviated to m.m.f. with a general symbol Fm.
The magnetomotive force is the force that creates the magnetic field. The m.m.f. acts like the electromotive force in an electric circuit and is the force necessary to set up a magnetic flux in a magnetic circuit.
The m.m.f. is dependent on the current flowing in a conductor, and the magnetic field of a solenoid is dependent on the number of turns of the solenoid. The field strength of a coil is therefore proportional to the product of the current and the number of turns in the coil.
In pure SI units, the m.m.f. unit is the ampere, because the number of turns in a coil or solenoid is considered dimensionless. In calculations, however, the number of turns has to be included.
Generally within the electrical trades, an m.m.f. quantity will be given directly as ampereturns (abbreviated IN), and the units will be specified as ampereturns (At).
Where:
Example
If a current of 5 A is flowing in a coil of 120 turns, find the value of m.m.f. creating a magnetic flux.
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