MAGNETISM & ELECTROMAGNETISM 3.1.1 MAGNETIC … · magnetic effects of the electrons moving in their ... The susceptibility (Xm) ... manganese copper sulphate, liquid oxygen and solutions

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Magnetism & Electromagnetism htpp://www.allonlinefree.com

MAGNETISM & ELECTROMAGNETISM

3.1.1 MAGNETIC PERMEABILITYConsider the relation

β = µ (H + M) = µ0 (H + Xm H) = µ0 (1 + Xm) H = µ H

Where µ = µ0 (1 + Xm), is called the magnetic permeability of the material.

∴ β = µ H

Magnetic permeability (µ) of a medium is defined as the ratio of magnetic induction to the intensity of the magnetising field.

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µ = For vacuum Xm = 0 and µ = µ0

Hence magnetic induction in vacuum is β0 = µ0 H

The ratio =

is called the relative permeability µ0 Obviously µr = 1 + Xm

We may also classify magnetic materials in terms of the relative permeability µr

Diamagnetism : µr < 1 (For βi, µr = 1 - 0.00017)Paramagnetism : µr > 1 (For Al, µr = 1 + 0.00002)Ferromagnetsim : µr >> 1 (For pure Fe, µr = 1 = 200,000)

Magnetic Flux φ The magnetic flux φ through a surface S is defined as


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φ = ∫s = B.dS

It represents the lines of induction crossing surface S.The SI unit of magnetic flux is a weber (Wb)If B is uniform and normal to area A, φ = BAIf a = 1m2, φ = B i.e., magnetic induction is numerically equal to normal flux per unit area. Therefore, it is also called magnetic flux density.

Magnetic FluxUnit of Magnetic Flux density is Tesla. Tesla id the density of 1 Wb of magnetic flux per metre square.

3.1.2 What are the properties of the lines of force, also state the care and maintenance of the permanent magnet?

Ans. Following are the properties of the magnetic lines of force:

1 All the lines of force starts from the north pole and terminates to south pole outside the magnet and from south to north inside the magnet.


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2. There is no perfect insulator for the lines of force.3. All the lines of force try to follow the shortest path and exhibit the elastic nature.4. The lines of force do not cross each other.5. It produces the effect of magnetic shielding if a

closed magnetic ring is placed between two poles the maximum lines of force will complete its path through the ring and a minimum through the air.

6. The magnetic lines of force produces the induction effect. As the soft iron bar magnetises when the permanent magnet is brought near it.

Care and maintenance: If the molecules of the permanent magnet are dc-arranged then the magnet is htpp://www.allonlinefree.com

3.1.2

Bar MagnetSolt Iron piece

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demagnetised so the following precautions should be taken:(i) It should he used properly and should not be thrown.(ii) It should not be heated up.(iii) It should not be hammered (iv) If a pair of magnets is kept, the keepers should

be used and magnets should be kept facing the opposite polarity.

3.1.3 TYPE OF MAGNET

Q What are the different types of magnets?Ans. These are the following types of the magnet.a) Natural Magnet b) Artificial magnet

(a) Natural Magnet:A substance is found in the nature which exhibits the property of attracting the iron and its fillings, simultaneously the property of directing north and south. It is in the shape of a stone. In the ancient era it was used by the navigator for direction purposes. It is known as leading stone or Iode stone.


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(b) Artificial magnet:The magnets which are prepared by the human beings by artificial means like touch method etc. are known as artificial magnets. These are prepared by iron or steel.

The artificial magnets are of the following types:(i) Temporary magnet(ii) Permanent magnet. (i) Temporary magnets:

The magnets which loses their magnetism as soon as the magnetising means or force is removed. All the electro magnets arc the temporary magnets. The metal used in this case is the soft iron. The temporary magnets are used in electric bell, buzzers, bell indicator, etc.


3.1.3

Natural magnet

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(ii) Permanent magnets. The permanent magnets are those which retain their magnetism for a long time. It is observed that if a piece of hard steel is magnetised, it acquire a substantial magnetism which it retains for an indefinite time. Such magnets are permanent magnets. The material used for permanent magnets are tungsten steel, high carbon steel and other hardened steel etc.

Shapes:


3.1.4

Temporary magnet

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There are the different shapes like bar magnet, horse shoe magnet U-shape magnet and magnetic needle.

3.1.4 MAGNETIC PROPERTIES OF MATERIAL

Now in this section sonic discussions are necessary on magnetic properties of matter. Infact materials can be classified generally as (1) Diamagnetic, (2) Paramagnetic and (3) Ferromagnetic. However magnetic properties of most materials differ so little from the magnetic properties of the free space that they are of no


3.1.5

Shape of permanent magnets

Dar Magnet

Horse Shoe Magnet

U-Shape Magnet

Magnetic Needle

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practical use in the construction of magnetic circuits.

(1) Diamagnetic Material. These materials hence permeabilities slightly less than the permeability of free space. Materials like silver, copper and hydrogen for example are Diamagnetic.

(2) Paramagnetic Material. These materials have permeability is slightly greater than that of free-space Materials like Platinum, Aluminum and Oxygen are paramagnetic.

(3) Ferromagnetic Materials. These materials have permeabilities much greater than space. Principal ferromagnetic material is IRON and various steel. But Cobalt and Nickel are also ferromagnetic and various alloys consisting of these elemental materials are used for special purposes as explained above. Theory of Diamagnetic, Paramagnetic Ferromagnetic Material. Now a brief discussion will be made to explain the theory of the three type of Magnetic Materials just stated above. Infact the magnetic properties of materials can be explained by


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supposing that there exit within the atom themselves the equivalent of minute circuits in which currents flow. However in addition to the magnetic effects of the electrons moving in their orbits about the nucleus of the atom, which will be equivalent of currents, the electrons themselves are believed to spin about their own axes, and thereby also to produce magnetic effects then the magnetic behaviour of any atom of any particular element is determined by the combined effect, of all the orbital motions and all the electrons spin within the atom. As there is the possibility of the orbital motions or the spins having such senses and such orientations or to partially or wholly, neutralise one another’s effect, it is not infact surprising that atoms of various elements possess widely different magnetic properties. An atom in which the neutralisation of all magnetic effect is complete would possess no magnetic moment which means - no torque would act on such an atom to orient it in any particular way in a magnetic field. Hence Magnetic moment is a measure of the extent to which atoms of any particular substance are magnetic.


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In case of diamagnetic material, when it is placed in a magnetic field, instead of the atom being oriented so as to aid the field the magnetic axis of each atom apparently takes up a processional motion about the direction of the applied field, as the axis of a spinning top processes about the vertical. And procession can be shown to have the same effect as would the realignment of the atoms in such a way as to oppose the applied field. Hence there is a decrease in flux density without any change in magnetic field intensity, and the permeability of the material hence is slightly less than the permeability of Space.

As a paramagnetic material is placed in a magnetic field the atom or molecules in case of gases are oriented just as small current-carrying loops would be. Then they contribute their bit to the effect of the current that set up the field, and this increases the flux-density without any increase in magnetic field intensity. The permeability of the material therefore is slightly greater than the permeability of space.

However, it is not essential that the entire atom change its angular B portion in the process of being htpp://www.allonlinefree.com

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oriented. Infact orientation can be accompanied by certain electron spin or orbits within the atom realigning them so that their magnetic effects coincide with the applied field.

In case of Ferromagnetic Materials, the atoms instead of acting independently appear, to be grouped magnetically into what are called ‘domain’, which may contain as many as 1015 atoms, and all of the atoms in a domain are supposed to be aligned in such a way that their magnetic effects are all in the same direction. Moreover the atoms are interlocked in such htpp://www.allonlinefree.com

3.1.6

G.H Curve of Ferromagnetic Material

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a way that their magnetic effects are all in the same direction, and the atoms are so interlocked within the domain that the realignment of any must mean the realignment of all. Hence a single, large magnetic moment substituted for a larger number of small independent ones.

It have been seen that at a temperature between 400° and 700° C, any specimen of iron or steel loses its ferromagnetic properties. Infact this is due to the thermal agitation becoming so great that the regimentation of individual atomic magnetic moments into domains no longer exists. The temperature at which this occurs is known to be the Curie Point.

However, the flux density will be substantially increased by the contribution of the domain of the ferromagnetic material above it would be in free space for the same field intensity. Infact the rate at which the flux density increase with magnetic field intensity will vary widely with the material and the field intensity itself.


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3.1.5 PROPERTIES OF DIAMAGNETIC MATERIALSi) For diamagnetic substances µr is slightly less than unity.ii) The susceptibility (Xm) of a diamagnetic material

has a low negative value. It is independent of temperature.

iii) In an external magnetic filed, they get magnetised in a direction opposite to the field and so they have a tendency to move away from the field.

iv) If suspended freely, they set themselves ⊥ to the field.

Properties of paramagnetic materials(i) These substances have µr > and Xm + ve.

The susceptibility decreases with rise in temperature.

(ii) In an external magnetic field these substances get magnetised in the direction of the field. Hence they move from weaker to stronger part of the external field.

(iii) If suspended freely, they set themselves to the field.


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Platinum, aluminum, chromium, manganese copper sulphate, liquid oxygen and solutions

of salts of iron and nickel are examples of paramagnetic substances.

Properties of ferromagnetic materials

(i) The values of µr and Xm of these materials are very large.

(ii) They get strongly magnetised in the direction of the external field and so they are strongly attracted by magnets.

(iii) They set themselves parallel to the external field if suspended freely.

(iv) These materials exhibit the phenomenon of hysteresis.

(v) As temperature increases, the value of Xm

decreases. Above a certain temperature known as Curie temperature ferromagnetics become paramagnetics.

Iron, nickel and cobalt are some examples of ferromagnetic substance.


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There exist two other types of magnetism, closely related to ferromagnetism. These are antiferromagnetsim and ferrimagnetism.

Explanation Of Diamagnetism Diamagnetism occurs in those substances whose atoms consist of an even number of electrons. The electrons of such atoms are paired. The electrons in each pair have orbital motions as well as pin motions in opposite sense. The resultant magnetic dipole moment of the atom is thus zero. Hence when such a substance is placed in a magnetic field, the field does not tend to align the atoms (dipoles) of the substance. The field however, modifies the motion of the electrons in orbits which are equivalent to tiny current-loops. The electron moving in a direction so as to produce a magnetic field in the same direction as the external field is slowed down, while the other is accelerated (Lena’s law). The electron pair and hence the atom thus acquire an effective magnetic dipole moment which is opposite to the applied field. Hence for diamagnetic materials M is opposite to H. So the susceptibility Xm of a diamagnetic substance is negative and is very small.


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Explanation Of ParamagnestimIn paramagnetic materials, the magnetic fields associated with the biting and spinning electrons do not cancel out There is a net intrinsic it in it. The molecules in it behave like little magnets. When such substance is placed in an external magnetic field, it will turn and line up as axis parallel to the external field. Thus it tends to move further into field. i.e., there is force of attraction. The diamagnetic force of repulsion is also present, but it is not so strong a-s the attracting force g from the magnetic properties of the material. Since M and B (and H) arc in the same direction in paramagnetics the susceptibility Xm is positive. When a paramagnetic substance is heated, the thermal agitation of its atoms increases. So the alignment of the dipoles becomes more difficult. This is why the magnetisation of paramagnetic substances decreases as the temperature of the substance increases. Xm

∝ 1/T.

Explanation of FerromagnetismFerromagnetic substances are very strongly magnetic. The best-known examples of ferromagnets are the htpp://www.allonlinefree.com

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transition metals Fe, Co. and Ni. A ferromagnet has a spontaneous magnetic moment a magnetic moment even in zero applied field. The atoms (or molecules) of ferromagnetic materials have a net intrinsic magnetic dipole moment which is primarily due to the spin of the electrons. The interaction between the neighbouring atomic magnetic dipoles is very strong, It is called spin exchange interaction and is present even in the absence of an external magnetic field, it turns out that the energy of two neighbouring atomic magnets due to this interaction is the least when their magnetic moments are parallel lime neighbouring magnetic moments are therefore, strongly constrained to take parallel orientation. This effect of the exchange interaction to align the neighbouring magnetic dipole moments parallel to one another spreads over a small unite volume of the bulk. This small (1 —0.1 mm across) volume of the hulk is called t domain. All magnetic moments within a domain will point in the same direction, resulting in a large magnetic moment. Thus the bulk material consists of many domains. The domains are oriented in different directions. The total magnetic moment of a sample of the substance is the vector sum of the magnetic moments of the component domains.htpp://www.allonlinefree.com

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If an unmagnetised piece of ferromagnetic material, the magnetic moments of the domains themselves are not aligned. When an external field is applied, those domains that are aligned with the field increase an size at the expense of the others. In a very strong field, all the domains are lined up in the direction of the field and provide the high observed magnetisation.

If a ferromagnetic material is heated to a very high temperature, the thermal vibrations may become strong enough to offset the alignment within a domain. A such temperature, the material loses its ferromagnetic property and behaves like a paramagnetic material.


3.1.7

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The critic temperature above which a ferromagnetic material becomes a paramagnetic is called the Curie temperature.

3.1.6 RELATION INDUCTION (B) The magnetic induction is defined through its action on a moving charge. If a positive test charge q moving with velocity v through a point in a magnetic filed experience a force F, then the magnetic induction B at that point is defined by

F = q v x BThe magnitude of the magnetic induction = B =

3.2.1 MAGNETIC EFFECT OF ELECTRIC CURRENT (ELECTRO

MAGNETISM)A magnetic field is set up all along the length of the conductor when an electric current flows through a conductor. In the Fig. 8.6 the magnetic effect of electric current flowing through a conductor is being illustrated. In fact the production of magnetic field by the current


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carrying conductor is shown by an experiment where small iron particles (like iron filings) are sprinkled on a card board placed perpendicularly through the wire (conductor) carrying current. It is seen that the moment the current starts flowing through the wire the iron particles arrange themselves in circles around the wire, which proves that a circular magnetic field exists around current carrying conductor. Therefore it is noted that a circular magnetic field exists around current carrying conductor.

Therefore it is noted that

(1) The magnetic lines of force are circular in a plane perpendicular to the current.htpp://www.allonlinefree.com

3.2.1

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(2) The field nearest the conductor is strongest, and becomes weaker further and further away from the conductor.

(3) When the current flowing through the conductor increases, the magnetic field also increases, that is becomes stronger.

(4) When the current direction of flow is reversed, the direction of the field is also reversed.

3.2.2 MAGNETO MOTIVE FORCE (MMF) The magnetic pressure which drives or tends to drive Magnetic flux through a magnetic circuit is called Magneto Motive Force (MMF)

MFF is, infant, equal to the work done in joules in carrying a unit magnetic pole once through the entire magnetic circuit and it is measured in Ampere-Turns, as MMF is developed or produced by passing electric current thorough a wire of several number of Turns.

mmf = Current (in Ampere) x (No. of Turns) = AT


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Moreover MMF in magnetic circuit can be compared to EMF in an electric circuit. Whereas in case of MMF it is magnetic pressure,, in case of e.m.f. it is electric pressure.

Ampere-Turn is therefore is given by the product of current in Ampere and No. of Turns, and it is the unit of m.m.f.

3.2.3 FIELD INTENSITY / MAGNETISING FORCE

Filed Intensity or Magnetising Force, represented by H, at a point with in a magnetic field is numerically equal to the force experience by a N pole of one Weber placed at that particular point.

To explain the matter clearly, say we have to find the field intensity at a point P at a distance d metres from a pole (of a magnet) of m webers. Now, as per Coulombs Law force, F acting on the unit pole placed at P is determined by,

F = = Newton (as µr = 1 for air)


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∴ H = Field Intensity = N/ Weber or AT/m

(Ampere turns per metre which is same as N/Wb)

Therefore, the magnetic force acting on a unit pole at the point P is the Magnetising Force, or Field Intensity or Magnetic Strength at point P, is H =

Field Intensity, H is a force and hence, it is a vector quantity having both magnitude and direction. Therefore, say, it a magnetic pole of m Wb is placed in a uniform Field Intensity or Magnetising force of H N / Wb (or AT /m), the force acting on the pole is mH Newtons. As per the Law of Magnetic Force, we know (it should be noted here) that the magnetic force between two magnetic poles placed in a medium is (1) directly proportional their pole strengths, (2) inversely proportional to the absolute permeability of the surrounding medium and also (3) inversely proportional to the square of the distance between two magnetic poles placed in the medium.

3.2.4 EXPERIMENT TO DRAW B-H CURVE (BALLISTIC METHOD)htpp://www.allonlinefree.com

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Circuit DescriptionA specimen of the given ferromagnetic material is taken in the form of a ring (Rowland ring) the experimental arrangement.

A primary coil P1 is wound closely over the specimen ring. This winding is connected in series with a battery B, an ammeter A, a rheostat R1 and a resistance R’ through a reversing key K and a two-way key K1. A tap key K’ connected across R’ facilitates either its Inclusion to removal from the circuit. The secondary winding S1 over the specimen consists of a few’ turns of closely wound wire. This winding S1 is connected in series with a rheostat R, a ballistic galvanometer and tile secondary winding 2 of a standard solenoid through a key K2. K8 is the damping key across the ballistic galvanometer. P2 is the primary winding of the standard solenoid. The two way key K1 connects either P1

or P2 to the battery circuit.

Theory:Number of turns of the winding P1 = µ1

turns per metre htpp://www.allonlinefree.com

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Total number of turns of the winding S1 = µ2

turnsNumber of turns of the winding P2 = µ3

turns per metreTotal number of turns of tile winding S

= µ4 turnsArea of cross-section of the specimen = A Sq. metresArea of cross-section of the standard solenoid = a Sq. metresWhen the key K1 is closed to the left, a current I passes through the magnetising the ring. Then

The intensity of the magnetising field = H = η1i….. (1)

The magnetisation of the specimen develops a magnetic flux density B inside the ring. Then

The total flux linked with the secondary = φ = η2

BA

This is the change of flux in the secondary. It sets up an induced emf in the secondary circuit.


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If R is the total resistance of the secondary circuit, the charge passing through the ballistic galvanometer.

q = η2 BA/R

If θ is the first throw of the ballistic galvanometer coil, then

q = η2BA/R = Kθ (1 + λ/2)

Where K is the ballistic constant and λ the logarithmic decrement of the ballistic galvanometer.

To Eliminate K and λA known current i/is passed through the primary of the standard solenoid by closing the key K1 to the right.

Magnetic flux linked with the secondary = φ = µ0η3i/

aη4 Wb


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This change in the magnetic flux sends a charge q/ = through the galvanometer.

If θ / is the first throw in the galvanometer coil, then

q/ = = Kθ / 1 + Dividing Eq. (2) BY Eq. (3) we have

=

or B = = Wb/m2

Eq (4) gives the magnetic induction B induced in the specimen corresponding to the magnetic intensity H, given by Eq. (1).

Procedure The key K1 is first closed to the left and the resistances R1 and R/ are decreased until on closing the commutator K, the galvanometer gives a full scale deflection from the zero. The current required to do this is noted and is used as maximum current in the main experiment.


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The residual magnetism in the specimen is reduced to zero as follows: The galvanometer circuit is first broken and the resistances R1 and R/ are reduced to the minimum. The current passing through the primary of the ring solenoid is then reversed many times by means of the commutator K and R and R/

are gradually increased until the current which is reversed is very small.

The galvanometer is again put in the circuit by closing key K2. The key K/ is closed and resistance R1 is given a value corresponding to the maximum current. The commutator K is closed to the right and the first throw θ1 of the galvanometer is noted. The current i is also noted from the ammeter. The values of B1 and H1 are calculated by using Eqs. (4) and (1) respectively. The corresponding point can the B-H curve.

The galvanometer circuit is again broken and the specimen is again demagnetized by reversing rapidly the commutator K as described before. The ballistic galvanometer is again put in the circuit. Now R/ is given a small value and K/ is opened.htpp://www.allonlinefree.com

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The magnetising force is thereby decreased to H2

producing a ballistic throw θ2 in the galvanometer. This throw corresponds to a decrease in induction. B1- B2.

The value of magnetising field H2 is calculated by noting ammeter reading. The corresponding point on the graph is denoted by the point b. This process is repeated by gradually increasing R/ until current and hence H becomes zero. The graph corresponding to these readings is ac. After each measurement, the specimen is returned to the state a by the reversal of maximum current. Hence point a works as the reference point.


3.2.3

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The key K/ is now closed and commutator is reversed several times and finally left to the right. R/ is given a large value and galvanometer is again put in the circuit. The commutator K is then thrown over to the left and at the same time K/ is opened so that the current is reversed and at the same time made of small value. This gives a point on the part cd of the curve. The starting point is again a and change in magnetic induction is measured every Lime. The process is repeated in many steps until finally R/ is zero when the point e on the curve is reached.

The part efga can be drawn by symmetry. or by repeating the experiment using e as the reference point and leaving the commutator now on the left.

3.2.6 MAGNETIC HYSTERESIS

If a magnetic substance is magnetised in a strong in age field, it retains a considerable portion of magnetism r the magnetic force has been withdrawn. The phenomenon of lagging of magnetisation or induction flux it behind the magnetising force is known as magnetic hysteresis.


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Let a core of specimen of iron be wound with a number of turns of a wire and current be passed through the solenoid. A magnetic field of intensity H proportional to the current flowing through the solenoid is produced. Let magnetising force H is increased from zero to a certain maximum value and then gradually reduced to zero. If the values of flux density B in the core corresponding to various values of magnetising force H are determined and B-H curves arc drawn for increasing and decreasing values of magnetising force en it will be observed that 13-H curve obtained for decreasing values of H lies above that obtained for increasing values of Ii.

While decreasing the magnetising force H. when H is brought to zero the induction density B, is represented by OC and is called as residual magnetism. The power of retaining residual magnetism is called the retentively of the material.


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Now if the direction of flow of curs rent is reversed, the magnetising force H is reversed. Let the current be increased in the negative direction until the induction density B becomes zero. At this instant i.e. when B = 0, the de magnetising force H = OD, which is required to neutralize the residual magnetism and is known as coercive force. If the demagnetising force H is further increased to the previous maximum value and again gradually decreased to zero, reversed and further increased in original or positive direction to the maximum value, a closed loop ACDEFGA is obtained which is usually known as hysteresis loop or magnetic cycle. It is to be noted that the hysteresis loop that B lags behind H. The two never attain zero value simultaneously.


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Hysteresis is especially pronounced in materials of high residual magnetism, such as hard steel. In most cases, hysteresis is a liability as it causes dissipation of heat, waste of energy, and humming due to change in polarity and rotation of element magnets in the material.

Hysteresis loops for hard steel, wrought iron and cast steel and for alloyed sheet steel.


3.2.5

3.2.4

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Loop (a) is for hard steel. Due to its high retentively power and large coercive form, this material is well suited for permanent magnets. Since the area of hysteresis loop — hard steel is large, hard steel is not suitable for rapid reversals of magnetisation. C’ alloys of steel, aluminum and nickel known as alnico alloys are extremely suitable for permanent magnets.

Loop (b) is for wrought iron and cast steel which rises steeply. Hence these material have high magnetic permeability and good retentively, therefore, these materials an’ suitable for cores of electro-magnets.

Loop (e) is for iron, low carbon steel, silicon alloys, and Permalloy or Mumetal sheets. Since the permeability of these materials is very high and hysteresis losses are very low, these materials are most suitable for transformer cores and armatures, which are subjected rapid reversals of magnetisation. Silicon alloys and Permalloy (78.5% Ni; 21% iron with small quantities of copper, molybdenum, chromium,


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cobalt and manganese etc.) are better for us as compared to iron and low carbon steel.

3.2.7 FARADAY’S LAW OF ELECTROMAGNETIC INDUCTION

It is an experimental fact that an em.f is induced in a circuit when the net magnetic flux enclosed by the circuit changes with respect to time. This fact was first demonstrated by Michael Faraday one of the experiments made by Faraday. When the switch was closed he observed a deflection in the galvanometer connected to the second circuit.


3.2.6

Faraday’s experiment set up

MAGNET

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When the switch was opened he again observed a deflection but this time in a reverse direction. shows another circuit arrangement used by Faraday to study the production of electricity from magnetism. When the magnet was moved towards the coil or the coil was moved towards the magnet, the galvanometer registered a deflection. From his experiments Faraday formulated the following law known as Faraday’s law of electromagnetic induction.

e =

=

Where e denotes that e.m.f. induced in the winding having a flux linkage of λ weber turns, N is the number of turns, flux φ is in webers and t is time in seconds.

3.2.8 MAGNETIC FIELD DUE TO A CURRENT CARRYING CONDUCTOR


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In 1819 it was discovered Danish Physicist, Hans Christian Oersted that an electric current is always accomplished by certain magnetic effects.

Oersted found that when current is passed through a conductor placed above the magnetic needle, the needle turns in a certain direction. He also found that when the direction of flow of current is reversed the magnetic needle also deflects in opposite direction.


3.2.7

No. Current Flow(a)

Current Flowing from A to B(b)

Current flowing from B to A(c)

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Further investigation showed that the field around the current carrying conductor consists of lines of force, which encircles the conductor. It can be proved experimentally by passing a current carrying conductor AB in the card board and plotting the field with the help of magnetic needle on it.

It is observed that when the current is passed through conductor in upward direction, the direction of lines of force is counter-clockwise


3.2.8

Magnetic field Around A current Carrying conductor

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direction .observed from the top of the conductor) and when the current is passed through the conductor in downward direction, the direction of lines of force is clockwise observed from e top of the conductor).

The properties of the lines of magnetic induction around a current carrying conductor are summarized as below:

(1) Lines of magnetic induction are circles, symmetrical about, and concentric with the axis of the conductor.

(ii) The spacing between the lines of induction decreases as we move closer to the conductor.

(iii) The direction of lines of magnetic induction depends on the direction of flow of current through the conductor.

(iv) Magnetic induction or flux density depends upon the strength (or magnitude) of the current flowing through the conductor.

3.2.9 INDUCTORS (OR COILS)


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An inductor (or a coil) is an electrical component, which is manufactured with a specified amount of inductance. The inductors are used in tuning and filter circuits. They are used in radio receivers as a built in antenna coil to pick up radio signals. They are also used in transformers and coupled circuits to transfer (or couple energy from one circuit to another).

In many applications, the inductors are used to minimize alternating currents, while permitting flow of direct current. In such application, the inductor is called a choke. Thus we have chokes for audio frequency range and radio frequency range. These chokes are called audio frequency chocks (AFC) and radio frequency chocks (RFC). The inductors are generally specified with inductance value and current capacity.

3.2.10 INDUCTANCE OF A COIL The inductance of a coil can be determined from its physical Parameters. The physical parameters are length, area of cross section and number of turns of a coil.


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Let I = Length of core on which the coil is wound in metres (m)

A = Area of cross section of a core in square metres (m2)

N = Number of turns of coil µ0= Relative permeability of the core

material

Now the inductance of a coil is given by the relation.

L =

It is evident from the above relation that the inductance of coil depends directly on the permeability, area of cross section of the core and square of the number of turns of a coil. It also depends inversely on the length of the corer on which the coil is wound.

3.2.11 A chock coil consists of 150 turns wound upon a high permeability core. If µr = 3450, µ0 = 4π x 10-7 H/m, coil length is 5cm and cross


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sectional area is 5x10-4 m2. find the value of coil

inductance.

Solution: Given: N = 150; µr = 3540; µ0 = 4πx10-7

h/M; 1=5 CM = 0.05M AND a = 5x10-4m2

L = = H

= 1 H Ans.

32.12 SOLENOIDThe current carrying wire wound spirally in the form of helix about an axis, is known as solenoid or coil. Magnetic field produced due to current carrying solenoid is fairly uniform over a small region in the middle of the coil, it acts just like a bar magnet having north and south poles.

There are several methods used to determine the polarity of the solenoid.

htpp://www.allonlinefree.comSolenoid

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1. By Use of Compass Needle: If one of the poles (say north pole) of the compass needle be brought into close proximity to one of the poles of the current carrying solenoid I of unknown polarity the action of the compass needle will immaculately classify the pole as north or south depending upon whether the needle is repelled or attracted.

2. Helix Rule If the helix is held in right hand in such a manner that the finger tips point in the direction of flow of current and thumb is outstretched longitudinally along the coil, it will point towards north-pole.

3.2.12 FLEMING’S LEFT HAND RULEWhen the direction Flux in the Field and the direction of the current in the conductor are known the direction of Force can be determined by Fleming Lefty Hand Rule. In this method,


3.2.9

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stretch the Thumb, Finger and Middle Finer of the left Hands at right angles to each as illustrated. If the First Finger points towards the direction of Force (Motion) experienced by the conductor is given by the thumb.

Right hand cork screw Rule. Suppose when a Right-hand screw is turned to advance along the conductor in the direction of the current, then the direction of Rotation of the screw gives the direction of the line of Force

3.2.15 FARADAY’S LAWS OF ELECTROMAGNETIC INDUCTIONhtpp://www.allonlinefree.com

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First Law: Whenever the magnetic flux linking a coil or circuit changes, an e.m.f. is induced in it or whenever a conductor cuts magnetic flux an e.m.f. induced in that conductor.

Second Law: The magnitude of induced e.m.f. in a coil or a circuit is equal to the rate of change of flux-linkage. The magnitude of flux linkages is determined by the number of times a circuit is linked by the magnetic flux.

Now say if a coil has N number of turns and the magnetic flux 0 will link this coil N times, that is,

Flux linkages = Flux x Number of turns = φ N.Now lets us explain the matter as below:

Say a coil with N number of turns and the magnetic fluxes flowing changes from φ wb to to φ wb to φ2 in time t secs. However we know that Flux linkage is the product of number of turns and the magnetic fluxes linked with the coil.


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∴ Initial flux linkages (with initial flux, φ1) = N φ1

And Final flux linkages (with final flux φ2) = N φ2

Change of Flux Linkages = N φ2 -Nφ1

With time, the rate of change of Flux linkages = ∴As per the Faraday’s second Law of electro-magnetic induction, the induced e.m.f. is

e = ∝ volts,

e = K volts.

Now if K = 1 e =

We can now write this for expression of (a) in the differential form,

e = N volt


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e = - N. , the minus sign to the expression of (b) indicates that induced e.m.f. sets up current in such a direction so as to oppose the cause producing it as per the Lenz’s Law.


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3.2.13 LENZ’S LAWLenz’s Law is used to determine the direction of induced e.m.f. and hence current. As the Lenz’s Law states that the direction of electro-magnetically induced e.m.f. and hence current always is such that it opposes the cause producing it.

To explain the matter, say N-pole of a magnet approaches a coil. As the magnetic fluxes linking the coil is changing; an e.m.f. is induced in the coil, and, of course, this induced e.m.f. develops induced current in the coil. As per Lenz’s Law, the direction of this induced ‘current in the coil is such that it opposes the cause producing it, and have the induced current should flow in such a


3.2.12

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direction in the coil so that it develops the polarities which oppose the magnet. In fact this is possible. When the left face of the coil becomes N-poles, now, as we know the polarity of the coil face, the direction of the induced current can be easily found by applying Fleming’s Right Hand Rule. However when the N-pole of the magnet is approaching the coil, the induced current flows in the coil in such a direction that its left becomes N-pole. The result is that motion of the magnet (the cause) is opposed. And the mechanical energy spent in overcoming this repulsive force is converted into electrical energy which appears in the coil. Here we should remember that Lenz’s Law is, in fact, in accordance with the law of conservation.


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Fill in the blanks(1) Three solid elements possess permanent

magnetic properties namely iron, nickel and _________.

(2) Two like poles __________ each other.(3) Lines of forces start from _________ pole to _________ pole.(4) The formula expresses the flux density is B = __________.(5) The unit of relative permeability is ____________.(6) ___________ materials are those which are relatively easy to magnetize.(7) BH curve for air __________ line.(8) The unit of magnetic flux density is __________.(9) Aluminium is classified as _______ material.(10) A permanent magnet will __________ attract copper.

Answers


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1. Cobalt 2. Repel 3. North-South4. φ/A 5. neon 6. Ferromagnetic7. Straight 8. Web/m2 9. Paramagnetic10. not

True or False(1) Temporary magnet can be made from iron.(2) Two unlike poles repel each other.(3) The lines of forces are invisible.(4) β denotes the flux density.(5) A permanent magnet used in electric bell.(6) Magnetic intensity denoted by MI.(7) Platinum is a paramagnet.(8) The value of permeability of free space is 4π*10-

7 w/Am.(9) The permeability of platinum is 100(10) Electromagnets made by cobalt.

Answers

1. True 2. False 3. True4. True 5. False 6. False7. True 8. True 9. False10. False


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Multiple Choice Questions(1) The opposition so establish the magnetic field in a material is known as

a) Inductance b) Reluctance c) Flux density

(2) Two lines of forcesa) Intersect each other b) Never intersect each other c) Collect each other

(3) Fe3O4 is a a) Permanent magnet b) Artificial magnet c) Natural magnet

(4) The material bismuth is aa) Diamagnetic b) Ferromagnetic

c) Paramagnetic

(5) The ratio of B and H is calleda) Relative permeability b) Permeability


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c) Absolute permeability

(6) Ratio between MMF to magnetic flux is calleda) Reluctance b) Inductance

c) Capacitance

(7) The force of attraction is maximum ata) Center of magnet b) Poles of magnet c) None of these

(8) Copper and mercury is aa) Paramagnetic b) Ferromagnetic

c) Diamagnetic

(9) Ferromagnetic materials havea) High permeability b) Low permeability c) Constant permeability

(10) The unit of flux density isa) W/m2 b) Tesla c)

Both a and bAnswers

1. b 2. b 3. chtpp://www.allonlinefree.com

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4. c 5. c 6. a7. b 8. c 9. a10. c


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