### INTRODUCTION TO MAGNETIC MATERIAL

** **

The magnetic material are those in which a state of magnetization can be induced. When it is magnetized, it creates a magnetic field in the surraunding space. Magnetic materials play an important role in electronic engineering. Magnetic materials are used in magnetic circuits, in electromagnets, machines, transformer, saturable reactors, relays and many instruments. The electronic engineers must be well versed with the characteristics of the magnetic materials, so that they choose the proper material for the construction of adesired device.

All the substance found in nature posses same magnetic properties and interacts with an external magnetic field. The magnetic properties of a substance depend on the magnetic properties of the individual elementary particles, the structure of atoms and molecules and their groupings. Studies on the magnetic properties of micro particles reveal that the magnetic behaviour of atoms largely depends on that of electrons. The magnetism of other particles is insignificant. Thus the magnetic moment of the atomic nucleus of approximatelyone thousandth to that of the electronic shell of the atom. The magnetic moment of an electron arises due to its orbital, revalutian and twining (spin) motian.

### MAGNETIC PROPERTIES

Magnetic Permeability:

The permeability for the magnetic materials is the criteria for selecting them.

For dielectric material

D=e_{f}_{ }e E

e_{f}=Absolute permitivity fr free space 8.854x10^{-12}_{ }flm

e =Absolute permitivity

E = Electric intensity E is Volt /meter

D = Electric dispalcement and similarity for the magnetic material we have.

B =m _{0 }m _{r }e H

Where

m _{r}= m **/**m _{0}

m _{r }= Relative permeability

m _{0 }= Permeability of Vacuum

m _{ }= Permeability of the medium in henry per meter.

m _{0 }= 4 x 10^{-7} henry per meter.

B= Magnetic flux density in weber / m^{2}^{}

If a magnetization curve of magnetic material specimen between the flux density B and the field intensity H is plotted by making the use of the following circuit.

The flux linked is Φ. If "A' is the cross-sectional area of the specimen anchor ring then,

B = Φ/A

And H = NI/L_{m}

A = Area in m2

H = uniform magnetic field of strength in Newton/wb

Lm = Mean length of magnetic flux

The fiat section of the B - H curve is represented by an equation given by

B = H /(a+bH) B = flux density in wb/m^{2}

Where,

a = hardness constant is the measure of the value H, necessary to attain given

fraction saturation.

b = 1/Bs

Where Bs is the saturation density of the material.

**Retentivity: **The residual flux density Br on the loop is called retentivity.

**Coercivity:** The coercive force, which is required to reduce B to zero, is called the coercivity.

**Energy Product: **The maximum BH product is known as energy product. It is the quantity of importance for permanent magnetic materials.

Fig 5.2

Where, N = Number of turns on the specimen

Lm = Mean length of magnetic flux

p D (D = Diameter of Ring) Current in ammeter.

The graph of "B' against "H' is shown.

m_{r }=_{ }B_{ }/ m _{0} H

= B / 4p x 10^{-7} H

m_{max }= B_{m} at point A

H_{m}

Permeability of a magnetic material is

m_{ }=_{ }B_{ }/ H Where m = Absolute permeability in Henry/m

m_{r }=_{ } m _{0 }m_{r } Where m _{0} = Absolute permeability 4p x 10 H/m

**Reluctivity:**

The ratio 1 / m _{0 }m_{r }is called the reluctivity of a magnetic material.

**INDUCTOR**

Induced voltage is the result of flux cutting across a conductor. This action can be produced by physical motion of either the magnetic field or the conductor. When the current in a conductor varies in amplitude. The variations of current and its associated magnetic field are equivalent to motion of the flux. As the current increases in value, the magnetic field expands outward from the conductor. When the current decreases, the field collapses into the conductor. As the field expands and collapses with changes of current, the flux effectively expands and collapses. With changes of current the flux is effectively in motion. Therefore a varying current can produce induced voltage without the need for motion of the conductor.

This maving flux cuts across the conductor that is providing the current, producing induced voltage in the wire itself. Furthermore any other conductor in the field, whether carrying current or not, also is cut by the varying flux and has induced voltage.

lt is important to note that induction by a varying current results from the change in current, not the current value itself. The current must change to provide motion of the flux. Since inductance is a measure of induced voltage, the amount of inductance has an important eHect in any circuit in which the current changes.

**Self-inductance ****L**

The ability of a conductor to induce voltage in itself when the current changes is its selfinductance (or simple inductance). The symbol for inductance is **L, **and its unit is the Henry (1-1). One Henry is the amount of inductance that allows one volt to be induced when the current changes at the rat e of one ampere per second. The formula is

Where VL is in volts and di/dt is the current change in amperes per second. The self induced voltage across an inductance L produced by a change in current di/dt can be stated as

VL = L di/dt

Where VL is in Volts, L is in Henrys, and di/dt in Amperes per second.

The moving flux cuts across the conductor providing the current that produces induced voltane in the wire itsel1. Further any other conductor in the field, whether carrying the currcmt or not is alsa cut by the varying flux and has induced voltage. It** **is important to note that, induction by a varying current results from the change in current not the curmnt value itself. The current must change to provide motian to the flux.

Since inductance is a measure of induced voltage, the amount of inductance has an important eHect in any circuit in which the current changes.

Inductance of Coil:

In terms of physical construction of an inductor, the inductance depends on how a coil is wound.

- A greater number of turns (N), increases ' Li because more voltage can be induced. Actually i Li increases in proportion to N2. Double the number of turns in the same area and length, increases the inductance four times.

- More area 'A' enclosed by each turn increases i Li. This means a coil with larger turns has more inductance. The i L' increases in direct proportion to 'A' and as the square of the diameter of each turn.

- The “L” increases with the permeability of the core (m) For an air core, m is zero. With a magnetic core, “L” is increased by m factor, as the magnetic flux is concentrated in the coil.

- The ”L” decreases with more length for the same number of turns as the magnetic field then gets less concentrated.

Mui:ual inductance LM:

When the current in an inductor changes, the varying flux can cut across any other inductor nearby. This produces induced voltage in both inductors. In figure below, the eoil L_{1} is connected to a generatar that produces varying current in the turns. The winding L_{2} is not connected to L_{1} but the turns are linked by the magnetic field. A varying curront in L_{1} therefore induces voltage across L_{1} and thereby alsa in L_{2}.

If all flux of the current in L_{1} links all the turns of the coil L_{2}, then each turn in L_{2} will have the same amount of induced voltage as each turn has in Lı, Further the induced voltage V_{L2} can produce current in a load resistance connected across L_{2}

_{}

When the induced voltage produces current L_{2} its varying magnetic field induces vollage in L_{1}. The two coils L1 and L2 have mutual inductance, therefore current in one can induces voltage in the other.