NUMERICAL ON MAGNETIC SYSTEM -- EXAMPLES ON LEAKAGE AND FRINGING

Numerical on Magnetic System, Examples on Leakage and Fringing

NUMERICAL ON MAGNETIC SYSTEM -- EXAMPLES ON LEAKAGE AND FRINGING

Numerical on Magnetic System, Examples on Leakage and Fringing

WAVE PARTICLE DUALITY

Phenomena such as Interference, Diffraction and Polarisation can be explained by wave theory of light, however, phenomena such as photo electric effect and Compton effect can be explained by particle theory of light.

According to Planck Quantum Theory emission and absorption of light is not continuous but it is discrete and light is in form of small bundles or packets of energy which is called Photons. Hence light behaves as a wave on one hand and a particle on the other hand. This nature of light is known as dual nature and this property of light is known as Wave-Particle Duality.

On the basis of this dual nature of light, De-Broglie suggested that dual nature is not only of light but each moving material particle has dual nature. He assumed a wave to be associated with each moving material particle which is called the "Matter Wave".

POLYSTYRENE (PS)

Polystyrene can be made by polymerizing styrene monomers.

BIODEGRADABLE POLYMERS

Those Polymers which get decomposed by the process of biodegradation are known as biodegradable are known as biodegradable Polymers. The process which is carried out by biological systems usually bacteria or fungi, wherein a polymer chain is cleared via enzymatic activity is known as Biodegradation.

POWER SYSTEM -- INTRODUCTION TO POWER SYSTEM

Generating Station/Power Station

1) Conventional Systems: It includes thermal systems, hydro-electric system, and nucleus system.

2) Non-Conventional System: It includes tidal energy, Biogas energy.

Transmission System

1) Primary Transmission: The bulk of electric power is transmitted from the generating station to the major load centers by overhead lines at 132, 220 or 400 kV. This forms primary transmission system.

2) Secondary Transmission: At the substation, power is received at 132,220 or 400kv and is stepped down to 66 or 33kv depending upon the amount of power to be fed to a particular area.

Distribution System

Primary Distribution: It is also known as high voltage distribution. This part of the system operates at voltages somewhat higher than that of general utility and handless large blocks of power.

Secondary Distribution: The electric power from primary distribution lines is delivered to various substations. It is known as Low Voltage Distribution.

Utilization

The single phase residential load is connected between any one line and the neutral where as three phases 440 v motor load or furnaces etc. are connected across 3 phase lines directly.

MAGNETIZATION CURVES OR B-H CURVES -- HYSTERESIS LOOP

In B-H Curve, B stands for Magnetic Flux Intensity and H is Magnetizing Force.

TRANSISTOR CONFIGURATION

There are three configuration of Bipolar Junction Transistor (BJT). According to the way input is fed and output is taken from the BJT.

TYPES OF CONFIGURATION

i. Common Base Configuration - CB Configuration

ii. Common Emitter Configuration - CE Configuration

iii. Common Collector Configuration - CC Configuration

COMMON BASE CONFIGURATION

In Common Base Configuration Output is taken across Collector and Base.

COMMON EMITTER CONFIGURATION

In Common Emitter Configuration Output is taken from Collector and Emitter.

COMMON COLLECTOR CONFIGURATION

This circuit is used for impedance matching as it has input impedance and low output impedance. It is a unity gain amplifier.

BIODEGRADABLE POLYMERS

Those Polymers which get decomposed by the process of biodegradation are known as biodegradable are known as biodegradable Polymers. The process which is carried out by biological systems usually bacteria or fungi, wherein a polymer chain is cleared via enzymatic activity is known as Biodegradation.

POLYSTYRENE (PS)

Polystyrene can be made by polymerizing styrene monomers.

ION EXCHANGE RESINS

Ion exchange resins are cross lined polymer which contains some ions (Cations or Anions) which can be exchanged by the medium ions.

SYNTHETIC FIBRE -- SYNTHETIC FIBER

The Polymers possessing strong inter chain forces such as H-bonds which give them high tensile strength so that they can be spinned, are known as fibres.

Nylon-6 (Synthetic Fiber): It is obtained from the monomer caprolactum which in turn is obtained from cyclohexane (Petrochemical).

POLYMETHYL METHACRYLATE (PMMA)

Polymethyl Methacrylate can be made by polymerizing Methyl Methacrylate Monomers. Polymethyl Methacrylate has a good feature of transparency. Due to Transparency Nature PMMA is used to make lenses.

POLYTETRAFLUOROETHYLENE (PTFE)

Polytetrafluoroethylene can be made by polymerizing tetrafluoroethylene monomers.

RECTIFIER CIRCUIT

The circuit which converts AC in DC is called Rectifier Circuit

There are two types of Rectifier Circuit

i. Half Wave Rectifier

ii. Full Wave Rectifier

BRAGG'S EQUATION -- BRAGG'S LAW

X-rays are electromagnetic radiations with high energies and wavelengths of the order 〖10〗^(-10) meter. These rays can be diffracted whenever they meet barrier with one or more openings that is about the same size as the wavelength. The layers of atoms or ions in crystals are separated by a distance of around 100 or 200 pm, which is the right range to cause X-rays to be diffracted. Thus layers of atoms in a crystal act as a diffracting for X-rays.

BIODEGRADABLE POLYMERS

Those Polymers which get decomposed by the process of biodegradation are known as biodegradable are known as biodegradable Polymers. The process which is carried out by biological systems usually bacteria or fungi, wherein a polymer chain is cleared via enzymatic activity is known as Biodegradation.

ORGANOMETALLICS -- INTRODUCTION TO ORGANOMETALLICS

ORGANOMETALLICS COMPOUNDS

Organometallic Compounds are those compounds which contain one or more metal-carbon bonds. It may be noted that all the compounds containing carbon and a metal atom are not organometallics. To term a compound organometallic, It must contain one or more metal-carbon (M-C) bonds.

POLYSTYRENE (PS)

Polystyrene can be made by polymerizing styrene monomers.

POLYETHYLENE (PE)

Polyethylene can be made by polymerizing ethylene monomers.

RUBBER (ELASTOMERS)

In Elastomer, the Polymer chains are held together by the weakest intermolecular forces. These weak forces permit the polymer to be stretched. A few cross-links are introduced in between the chains which help the polymer to released to its original position after the forces is released.

Buna-S: Buna-S is obtained by the polymerization of butadiene and styrene in presence of sodium metal.

Buna-N: Buna-N is obtained due to co-polymerization of two parts of butadiene with one part of acrylonitrile in pressure of sodium metal.

BIODEGRADABLE POLYMERS

Those Polymers which get decomposed by the process of biodegradation are known as biodegradable are known as biodegradable Polymers. The process which is carried out by biological systems usually bacteria or fungi, wherein a polymer chain is cleared via enzymatic activity is known as Biodegradation.

CONDUCTING POLYMER

Polymers which can conduct electricity are called Conducting Polymers. Ordinary Polymers obtained by usual methods are nearly insulators. However, same specific polymers may act as conductors.

ADDITION POLYMERS -- ADDITION POLYMERISATION REACTIONS -- MECHANISM OF ADDITION POLYMERISATION -- ANIONIC ADDITION POLYMERISATION -- CONDENSATION POLYMERIZATION REACTION

ADDITION POLYMERS: The polymers which are synthesized using Addition Polymerization Reactions are known as Addition Polymers.

ADDITION POLYMERISATION REACTIONS: The Polymerization Reaction which involves joining of unsaturated monomers by breaking of Ï€-bonds in a chain like manner without elimination of any byproduct is known as Addition Polymerization Reaction.

CONDENSATION POLYMERIZATION REACTION: When Monomers contains two or more functional groups which react to form the polymer with release of small byproduct then the reaction is known as Condensation Polymerization Reaction.

Wish that the affinity of our past had exposed the best out of us. But on the contrary, our political system is heading towards futility. The most dismal situation is that we have become a subject of mockery in the western media too and without any astonishment most of us agree with: what the world is saying about us. I am no such person who feels enlightened by the derogatory remarks about my countrymen who happen to be the renowned politicians. But there is no escapism for this situation.

This country, famous for diverse religion and culture is being known for en-rooted corruption. It's a moment of sigh for each one of us and the blame game is not working either. Corrupts being alert, still follow their grotesque practice as they are more confident of their power. Censuring just the UPA is not much of a worthy idea. In fact, each person involved should be questioned and punished for this disparaging situation. What Anna Hazare and other renowned troops are doing is commendable but we being responsible citizens either watch them on TV and praise them or sometimes come out on streets shouting slogans. Our outcry has not yet made much of a difference because even politicians are aware "action speaks louder than words." My implication is not at all a violent one, just an appeal to fellow citizens to demonstrate their national love. Last year, witnessed an absurd situation, during the initial days of Anna Hazare's national program, one of his energetic follower wearing a cap by his name, crossed a red light (the act was intentional). It was a disgrace to Anna ji, as seeing this incidence a group poked fun at the leader and his counterparts. It was a sad moment, for all the other supporters, that young man had brought disgrace to our movement. Anyways, what I want to convey is, being the supporters of anti-corruption movement we have to be moralistic. Corruption is not just measured in monetary terms but any unethical act is a part of corrupt commotion. As little things make difference, so we should abstain from abiding law, dishonesty, deceiving and violence. In simple term, together we achieve which no one can achieve alone.

This country, famous for diverse religion and culture is being known for en-rooted corruption. It's a moment of sigh for each one of us and the blame game is not working either. Corrupts being alert, still follow their grotesque practice as they are more confident of their power. Censuring just the UPA is not much of a worthy idea. In fact, each person involved should be questioned and punished for this disparaging situation. What Anna Hazare and other renowned troops are doing is commendable but we being responsible citizens either watch them on TV and praise them or sometimes come out on streets shouting slogans. Our outcry has not yet made much of a difference because even politicians are aware "action speaks louder than words." My implication is not at all a violent one, just an appeal to fellow citizens to demonstrate their national love. Last year, witnessed an absurd situation, during the initial days of Anna Hazare's national program, one of his energetic follower wearing a cap by his name, crossed a red light (the act was intentional). It was a disgrace to Anna ji, as seeing this incidence a group poked fun at the leader and his counterparts. It was a sad moment, for all the other supporters, that young man had brought disgrace to our movement. Anyways, what I want to convey is, being the supporters of anti-corruption movement we have to be moralistic. Corruption is not just measured in monetary terms but any unethical act is a part of corrupt commotion. As little things make difference, so we should abstain from abiding law, dishonesty, deceiving and violence. In simple term, together we achieve which no one can achieve alone.

MAXWELL EQUATIONS IN INTEGRAL FORM

Consider the case of electromagnetic phenomena in free space in perfect dielectric containing no charge and no conduction current (j=0) for the case are the field equation become ........

ELECTROMAGNETIC WAVES IN A CONDUCTING MEDIUM

Electromagnetic Waves in a Conducting Medium: There may be conduction current in the medium but the charge density is zero everywhere.

PROPAGATION OF ELECTROMAGNETIC WAVES IN DIELECTRIC MEDIUM

1) In Dielectric Medium there is no Charge Carrier so Current Density will be zero.

2) If Dielectric Medium is Isotropic then Volume Density will be zero.

FUNDAMENTAL OF ELECTROMAGNETIC

PROPERTIES OF ELECTROMAGNETIC WAVES

1) Electromagnetic wave propagates.

2) In Vacuum Electromagnetic Wave moves with velocity.

3) Electromagnetic waves of different frequencies can exist. All such wave propagates with speed c.

4) No material particle moves with electromagnetic waves.

5) Electric field vector plays role of light vector.

TRANSISTOR CONFIGURATION

There are three configuration of Bipolar Junction Transistor (BJT). According to the way input is fed and output is taken from the BJT.

TYPES OF CONFIGURATION

i. Common Base Configuration - CB Configuration

ii. Common Emitter Configuration - CE Configuration

iii. Common Collector Configuration - CC Configuration

COMMON BASE CONFIGURATION

In Common Base Configuration Output is taken across Collector and Base.

COMMON EMITTER CONFIGURATION

In Common Emitter Configuration Output is taken from Collector and Emitter.

COMMON COLLECTOR CONFIGURATION

This circuit is used for impedance matching as it has input impedance and low output impedance. It is a unity gain amplifier.

CLIPPER CIRCUIT

Clipper is wave shaping circuits in which diodes are used to clip or cut off one or both extremities from the wave form of input wave or pulse.

EIGEN VALUES -- EIGEN VECTORS -- MODEL MATRIX -- DIAGONAL OF THE MATRIX

Eigen Values and Eigen Vectors Introduction, Model Matrix, Diagonal of the Matrix

PIN DIAGRAM OF IC 741 OPERATIONAL AMPLIFIER -- THE 741 OPERATIONAL AMPLIFIER

The IC 741 is supplied in 8-PIN 'Dual in Line' package without a pinout.

PIN 1 & 5 -- Not Connected Anywhere But for some frequency adjustment and to set the offset Voltage we use PIN 1 & 5

PIN 2 -- Inverting Input

PIN 3 -- Non Inverting Input

PIN 4 -- Negative Power Supplied in PIN 4

PIN 6 -- Output is taken in PIN 6

PIN 7 -- Positive Power is supplied in PIN 7

PIN 8 -- Not Connected

CAYLEY HAMILTON THEOREM

Every Square Matrix satisfies its own characteristics equations.

LINEAR DEPENDENCE AND INDEPENDENCE OF VECTOR

Linear Dependence and Independence of Matrices

Vectors (Matrices) X_1,X_2,X_3.............X_n are said to be dependent if

All the vectors (Row or Column Matrices) are of same order.

n -- Scalars Y_1,Y_2,Y_3.............Y_n exist such that 〖X_1 Y〗_1+ 〖X_2 Y〗_2+ 〖X_3 Y〗_3.............+ 〖X_n Y〗_n= 0 ............. Otherwise they are linearly independent.

CALCULATION OF CENTROID

PROCEDURE TO FIND CENTROID OF COMPOSITE AREAS AND LINES

Following steps are adopted to find co-ordinates of centroid of composite figures:

1) Select suitable co-ordinate axes if not given.

2) Divide given area/lines in to different parts having known area or length and known centriodal distances.

3) Check Symmetry of Figures

(a) If section is symmetrical about x axis we can find y directly without any calculations.

(b) If section is symmetrical about y axis we can find x directly without any calculation.

CENTRE OF GRAVITY, CENTRE OF MASS, CENTROID

CENTRE OF GRAVITY

Centre of Gravity (CG) of a body is a point through which the resultant of distributed gravity forces act irrespective of orientation of body.

CENTRE OF MASS

It is the point where entire mass of a body may be supported to be concentrated.

CENTROID

Centroid is defined as geometrical centre of body.

In general when density of material is uniform through the body the positions of centroid and centre of mass are identical. If density varies these two points will not coincide.

PARALLEL AND PERPENDICULAR AXIS THEOREMS

PARALLEL AXIS THEOREM

The Moment of Inertia of any plane area about any axis parallel to its centrodial axis is equal to summation of its moment of Inertia about centroidal axis and product of its area and square of distance between the two axes.

PERPENDICULAR AXIS THEOREM

Moment of Inertia of a plane area about any axis perpendicular to plane area is equal to sum of its moment of inertias about the two perpendicular axes lying in the plane of area. The perpendicular axis should pass through intersection point of axes lying in the plane of area.

MOMENT OF INERTIA, AREA MOMENT OF INERTIA, MASS MOMENT OF INERTIA

There are two types of Moment of Inertia:

1) Area Moment of Inertia

2) Mass Moment of Inertia

1) Area Moment of Inertia: Area Moment of Inertia is defined for plane figures (i.e. Rectangle, Triangle, Circle etc.) moment of inertia of a plane area about any axis is second moment of area about that axis.

2) Mass Moment of Inertia: Mass Moment of Inertia is defined for the bodies having mass like solid bodies i.e. (Cylinder, Cone, Sphere, Circular Plate etc).

Eigen Values and Eigen Vectors Introduction, Model Matrix, Diagonal of the Matrix

CALCULATION OF CENTROID

PROCEDURE TO FIND CENTROID OF COMPOSITE AREAS AND LINES

Following steps are adopted to find co-ordinates of centroid of composite figures:

1) Select suitable co-ordinate axes if not given.

2) Divide given area/lines in to different parts having known area or length and known centriodal distances.

3) Check Symmetry of Figures

(a) If section is symmetrical about x axis we can find y directly without any calculations.

(b) If section is symmetrical about y axis we can find x directly without any calculation.

LINEAR DEPENDENCE AND INDEPENDENCE OF VECTOR

Linear Dependence and Independence of Matrices

Vectors (Matrices) X_1,X_2,X_3.............X_n are said to be dependent if

All the vectors (Row or Column Matrices) are of same order.

n -- Scalars Y_1,Y_2,Y_3.............Y_n exist such that 〖X_1 Y〗_1+ 〖X_2 Y〗_2+ 〖X_3 Y〗_3.............+ 〖X_n Y〗_n= 0 ............. Otherwise they are linearly independent.

CAYLEY HAMILTON THEOREM

Every Square Matrix satisfies its own characteristics equations.

PIN DIAGRAM OF IC 741 OPERATIONAL AMPLIFIER -- THE 741 OPERATIONAL AMPLIFIER

The IC 741 is supplied in 8-PIN 'Dual in Line' package without a pinout.

PIN 1 & 5 -- Not Connected Anywhere But for some frequency adjustment and to set the offset Voltage we use PIN 1 & 5

PIN 2 -- Inverting Input

PIN 3 -- Non Inverting Input

PIN 4 -- Negative Power Supplied in PIN 4

PIN 6 -- Output is taken in PIN 6

PIN 7 -- Positive Power is supplied in PIN 7

PIN 8 -- Not Connected

CALCULATION OF MOMENT OF INERTIA, PROCEDURE TO FIND MOMENT OF INERTIA OF SOME STANDARD FIGURES

1) Moment of Inertia of Rectangular Area

2) Moment of Inertia of Hollow Rectangular Area

3) Moment of Inertia of Circle

4) Moment of Inertia of Semi-circle

5) Moment of Inertia of Quarter-circle

6) Moment of Inertia of Triangle

PARALLEL AND PERPENDICULAR AXIS THEOREMS

PARALLEL AXIS THEOREM

The Moment of Inertia of any plane area about any axis parallel to its centrodial axis is equal to summation of its moment of Inertia about centroidal axis and product of its area and square of distance between the two axes.

PERPENDICULAR AXIS THEOREM

Moment of Inertia of a plane area about any axis perpendicular to plane area is equal to sum of its moment of inertias about the two perpendicular axes lying in the plane of area. The perpendicular axis should pass through intersection point of axes lying in the plane of area.

MATRICES AND TYPES OF MATRICES

TYPES OF MATRICES

1) Row Matrix

2) Column Matrix

3) Null or Zero Matrix

4) Square Matrix

5) Diagonal Matrix

6) Scalar Matrix

7) Unit or Identity Matrix

8) Symmetric Matrix

9) Skew Symmetric Matrix

10) Orthogonal Matrix

11) Congugate Matrix

12) Unitary Matrix

13) Hermitian Matrix

14) Skew -- Hermitian Matix

15) Idempotent Matrix

16) Involutory Matrix

17) Equal Matrices: Two matrices are said to be equal if (1) they are of same ored. (2) The elements in the corresponding positions are equal.

18) Singular Matrix

ELEMENTARY TRANSFORMATION

There are two types of Elementary Transformation:

1) Row or Elementary Row Transformation

2) Column or Elementary Column TRansformation

PHASE DIAGRAM FOR WATER -- WATER PHASE DIAGRAM

Under normal conditions the system 'water' is a three phases, one component system. The three phase involved are liquid water, ice, water vapour. All these phases can be represented by one chemical entity H_2 O and hence one component of the system. The number of phases which can exist in equilibrium any time depends on the conditions of temperature and pressure. The phase diagram or PT graph of the system water/ice/vapour can be shown as ...

THE GIBBS PHASE RULE

Gibbs Phase Rule states that the degree of freedom of a system at equilibrium is related with its component and the total no. of phases by the relation

F = C-P+2

Where F is the number of degree of freedom, C is the number of components and P is the number of phases of system.

CHEMICAL THEORY OF CORROSION

The different types of theories are:

i. Chemical Theory (Dry Theory)

ii. Electrochemical Theory (Wet Theory)

CHEMICAL THEORY OF CORROSION

Such types of Corrosion occur due to the chemical action of following liquid metal at high temperature on solid metal or alloy. This type of corrosion is common in devices used for nuclear power. The corrosion reaction involves one of the following

i. Dissolution of a solid metal by a liquid metal

ii. Internal penetration of the liquid metal into the solid metal.

FUEL CELL

Fuel Cells are voltanic cells in which the reactants are continuously supplied to the electrodes. In other words, Fuel Cells are electrochemical devices in which the chemical energy of the fuel in directly converted into electrical energy. Depending on the type of fuel used, Fuel cells can be of the following types:

i. Hydrogen -- Oxygen Fuel Cell

ii. Hydrocarbon -- Oxygen Fuel Cell

iii. Methyl Alcohol -- Oxygen Fuel Cell

iv. Carbon Monoxide -- Oxygen Fuel Cell

v. Solid Coal -- Oxygen Fuel Cell

SECOND ORDER REACTION

A Reaction is said to be of Second Order if its reaction rate is determined by the variation of two concentration terms of reactants ...

INSTRUMENTS -- ESSENTIALS OF INDICATING INSTRUMENTS -- PERMANENT MAGNET MOVING COIL (PMMC)

Types of Instruments:

1) Absolute Instruments

2) Secondary Instruments

3) Indicating Instruments

4) Integrating Instruments

5) Recording Instruments

Essentials of Indicating Instruments:

1) Deflecting Torque

2) Controlling Torque

3) Damping Torque

PERMANENT MAGNET MOVING COIL INSTRUMENT:

PRINCIPLE: When a current carrying conductor is placed in a magnetic field, it experiences a force. The direction of force is given by Fleming's left hand rule.

Types of Instruments:

1) Absolute Instruments

2) Secondary Instruments

3) Indicating Instruments

4) Integrating Instruments

5) Recording Instruments

Essentials of Indicating Instruments:

1) Deflecting Torque

2) Controlling Torque

3) Damping Torque

PERMANENT MAGNET MOVING COIL INSTRUMENT:

PRINCIPLE: When a current carrying conductor is placed in a magnetic field, it experiences a force. The direction of force is given by Fleming's left hand rule.

INDUCTION TYPE INSTRUMENTS

The principle of operation of induction instrument is similar to that of induction motor. A rotating magnetic field is produced by the coils of the instrument. A aluminum disc is suspended near to the coil in which eddy currents are induced by rotating flux. The rotating flux interacts with the induced eddy current and produces torque which causes the aluminum disc to rotate.

ELECTRODYNAMIC OR DYNAMOMETER TYPE INSTRUMENTS

It is very similar to PMMC instruments except that the permanent magnet field is replaced by coils (usually 2 fixed air cored coils) which carry current to be measured. The coils are usually air cored to avoid hysteresis, eddy currents and other errors.

Deflecting torque is produced by interaction of magnetic fields. One field is due to current in fixed coil and other field is due to current in moving coil.

BALANCED SYSTEM AND UNBALANCED SYSTEM

A set of three sinusoidal voltages (or current) that are equal in magnitude but having a progressive phase differences of 120 degree constitute a balanced three phase voltage system. The three phase quantities are otherwise said to be unbalanced.

Phase sequence is the order or sequence in which the current or voltages in different phases attain their maximum values one after the other.

PHASE SEQUENCE OF 3 PHASE SUPPLY IS ESSENTIAL FOR: The direction of rotation of 3 phase induction motor depends upon the phase sequence of 3-phase supply, to reverse the direction of rotation; the phase sequence of the supply given to the motor has to be changed.

The parallel operation of 3-phase alternator and transformer is only possible if phase sequence is known.

3 PHASE POWER MEASUREMENT -- MEASUREMENT OF POWER IN THREE PHASE CIRCUITS

1) One Wattmeter Method

2) Two Wattmeter Method

3) Three Wattmeter Method

1) One Wattmeter Method

2) Two Wattmeter Method

3) Three Wattmeter Method

PIEZOELECTRIC EFFECT -- PRODUCTION OF ULTASONIC WAVES

When an AC Voltage is applied across a piezoelectric crystal such as Quartz Crystal, It vibrates at the frequency of the applied voltage. Vibration of maximum amplitude occurs at the natural resonant frequency of the crystal which is determined by physical dimension and by the way the crystal is cut. The Frequency is given by ...

ULTRASONIC WAVES -- THEORY OF ULTRASONIC WAVES

Waves in nature are of two types, Mechanical and Electromagnetic. Mechanical waves are longitudinal in nature and require a medium for its's propagation. Electromagnetic waves are transverse in nature and do not requires a material medium for their propagation. Sound waves are mechanical in nature.

Sound waves are classified according to the frequency range. Sound waves having frequency less than 20 Hz are known as infrasonic waves. Waves having frequency between 20 Hz and 20000 Hz lie in audible sound. Sound waves having frequency higher than human audible range or sound waves having frequency above 20 Hz are known as Ultrasonic waves or Supersonic Waves.

HYSTERISIS LOSS - B-H CURVE - DERIVATION FOR THE HYSTERESIS LOSS

In the state of Ferromagnetic Substances the magnetic domain form closed chain due to which the net magnetic moment of the substance is zero. When the substance is placed in an external magnetic field, the domains rotate and arrange themselves such that their magnetic moment becomes in the direction of external magnetic field. Work is done by the external magnetic field in this alignment. But on removal of the external magnetic field, these domains could not come back to their initial state and some magnetism is left within the substance. Hence some amount of energy is not returned back to demagnetization. Thus in each Hysteresis loop there is some loss in energy. This energy loss is called Hysteresis Loss.

MAGNETOSTRICTION EFFECT -- PRODUCTION OF ULTRASONIC WAVES

When a rod of ferromagnetic material is kept in magnetic field parallel to its length the rod suffer a change in its length. The change in length is independent of the direction of magnetic field. This phenomenon is known as Magnetostriction.

If the magnetic field is alternating and has frequency equal to the natural frequency of the rod, a large amplitude longitudinal vibration can be set up. The frequency of Oscillation is ...

FERROMAGNETISM -- EXPLANATION OF FERROMAGNETISM -- INTRODUCTION TO FERROMAGNETISM

Ferromagnetic Substance is such Paramagnetic substance which is highly magnetized in external magnetic field. Like Paramagnetic substance, atoms of ferromagnetic substance have a permanent magnetic moment and behave like tiny magnet. In Ferromagnetic substance, the atoms due to certain mutual interaction form innumerable small regions called domains. Each domain has 〖10〗^17 to 〖10〗^21 atoms whose magnetic axes are aligned in the same direction.

JACOBIAN

Let u, v are function of variables of x, y then the determinant ...

Let u, v are function of variables of x, y then the determinant ...

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

EXTREMA OF FUNCTIONS OF SEVERAL VARIABLES -- MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES

Let we have the function f(x,y) which have two variables x and y. We have to get the maxima and minima means either it is maxima or minima.

APPROXIMATION OF ERROR -- APPROXIMATION ERROR

Let x be a any physical quantity then ∂x is said to be say error in the present quantity x.or we can also say that ∂x is error which is known as Approximation Error. Now

∂x Absolute Error

(∂x )/x Relative Error

(∂x )/x ×100 Percentage Error

JACOBIAN PROPERTIES -- CHAIN RULE JACOBIAN

If u, v are the function of r, s and r, s be the functions of x, y then

(∂(u,v))/(∂(x,y))= (∂(u,v))/(∂(r,s)) × (∂(r,s))/(∂(x,y))

This is also called Chain Rule Property of Jacobian.

LANGEVIN THEORY OF DIAMAGNETISM

Diamagnetic substances are those which placed in an external magnetic field become weekly magnetized in a direction opposite to the magnetic field direction. So, Diamagnetic material possesses a small value of negative susceptibility which is independent of temperature.

Let us consider the case of single electron of charge e moving in circular orbit in an atom so the equivalent current of a single electron will be

I = ev

V is the angular frequency of electron motion.

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