Concept and Analogies of Magnetic Circuit

Term paper of ECE(basic electronics and electrical)

Name: aalok mallik
Reg no:11008765
Sec:Rk6002
Roll no:B55

.contents
1.History
2.Classification
3.Introduction of magnetic circuit
4.Concept
5.Analogies
6.Laws of magnetic circuit
7.Application
8.Referenece

Concept and analogies of magnetic circuit

HISTORY

As with all great discoveries the history of magnets is very colorful and interesting too.
The Shepherd Magnes
The most popular legend accounting for the discovery of magnets is that of an elderly Cretan shepherd named Magnes. Legend has it that Magnes was herding his sheep in an area of Northern Greece called Magnesia, about 4,000 years ago. Suddenly both, the nails in his shoes and the metal tip of his staff became firmly stuck to the large, black rock on which he was standing. To find the source of attraction he dug up the Earth to find lodestones (load = lead or attract). Lodestones contain magnetite, a natural magnetic material Fe3O4. This type of rock was subsequently named magnetite, after either Magnesia or Magnes himself.
The Greek & Chinese
The earliest discovery of the properties of lodestone was either by the Greeks or Chinese. Stories of magnetism date back to the first century B.C in the writings of Lucretius and Pliny the Elder (23-79 AD Roman). Pliny wrote of a hill near the river Indus that was made entirely of a stone that attracted iron. He mentioned the magical powers of magnetite in his writings. For many years following its discovery, magnetite was surrounded in superstition and was considered to possess magical powers, such as the ability to heal the sick, frighten away evil spirits and attract and dissolve ships made of iron!
People believed that there were whole islands of a magnetic nature that could attract ships by virtue of the iron nails used in their construction. Ships that thus disappeared at sea were believed to have been mysteriously pulled by these islands. Archimedes is purported to have used loadstones to remove nails from enemy ships thus sinking them.
People soon realized that magnetite not only attracted objects made of iron, but when made into the shape of a needle and floated on water, magnetite always pointed in a north-south direction creating a primitive compass. This led to an alternative name for magnetite, that of lodestone or "leading stone".
For many years following the discovery of lodestone magnetism was just a curious natural phenomenon. The Chinese developed the mariner's compass some 4500 years ago. The earliest mariner's compass comprised a splinter of loadstone carefully floated on the surface tension of water.
Early Discoveries
Peregrinus & Gilbert Peter Peregrinus is credited with the first attempt to separate fact from superstition in 1269. Peregrinus wrote a letter describing everything that was known, at that time, about magnetite. It is said that he did this while standing guard outside the walls of Lucera which was under siege. While people were starving to death inside the walls, Peter Peregrinus was outside writing one of the first 'scientific' reports and one that was to have a vast impact on the world.
However, significant progress was made only with the experiments of William Gilbert in 1600 in the understanding of magnetism. It was Gilbert who first realized that the Earth was a giant magnet and that magnets could be made by beating wrought iron. He also discovered that heating resulted in the loss of induced magnetism.
Oersted & Maxwell
In 1820 Hans Christian Oersted (1777-1851 Danish) demonstrated that magnetism was related to electricity by bringing a wire carrying an electric current close to a magnetic compass which caused a deflection of the compass needle. It is now known that whenever current flows there will be an associated magnetic field in the surrounding space, or more generally that the movement of any charged particle will produce a magnetic field.

There are various types of magnets depending on their properties. Some of the most well known are listed below.
Permanent Magnets
These are the most common type of magnets that we know and interact with in our daily lives. E.g.; The magnets on our refrigerators. These magnets are permanent in the sense that once they have been magnetized they retain a certain degree of magnetism. Permanent magnets are generally made of ferromagnetic material. Such material consists of atoms and molecules that each have a magnetic field and are positioned to reinforce each other.

Classification
Permanent Magnets can further be classified into four types based on their composition: 1. Neodymium Iron Boron (NdFeB or NIB) 2. Samarium Cobalt (SmCo) 3. Alnico 4. Ceramic or Ferrite
NIB and SmCo are the strongest types of magnets and are very difficult to demagnetize. They are also known as rare earth magnets since their compounds come from the rare earth or Lathanoid series of elements in the periodic table. The 1970s and 80s saw the development of these magnets.
Alnico is a compound made of ALuminium, NIckel and CObalt. Alnico magnets are commonly used magnets and first became popular around the 1940s. Alnico magnets are not as strong as NIB and SmCo and can be easily demagnetized. This magnet is however, least affected by temperature. This is also the reason why bar magnets and horseshoes have to be taken care of to prevent them from loosing their magnetic properties.
The last type of permanent magnets, Ceramic or Ferrite magnets are the most popular today. They were first developed in the 1960s. These are fairly strong magnets but their magnetic strength varies greatly with variations in temperature.
Permanent Magnets can also be classified into Injection Moulded and Flexible magnets. Injection molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties. Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.
Shape & Configuration
Permanent magnets can be made into any shape imaginable. They can be made into round bars, rectangles, horseshoes, donuts, rings, disks and other custom shapes. While the shape of the magnet is important aesthetically and sometimes for experimentation, how the magnet is magnetized is equally important. For example: A ring magnet can be magnetized S on the inside and N on the outside, or N on one edge and S on the other, or N on the top side and S on the bottom. Depending on the end usage, the shape and configuration vary.
Demagnetization
Permanent magnets can be demagnetized in the following ways: - Heat - Heating a magnet until it is red hot makes it loose its magnetic properties. - Contact with another magnet - Stroking one magnet with another in a random fashion, will demagnetize the magnet being stroked. - Hammering or jarring will loosen the magnet's atoms from their magnetic attraction.
Temporary Magnets
Temporary magnets are those that simply act like permanent magnets when they are within a strong magnetic field. Unlike permanent magnets however, they loose their magnetism when the field disappears. Paperclips, iron nails and other similar items are examples of temporary magnets. Temporary magnets are used in telephones and electric motors amongst other things.
Electromagnets
Had it not been for electromagnets we would have been deprived of many luxuries and necessities in life including computers, television and telephones. Electromagnets are extremely strong magnets. They are produced by placing a metal core (usually an iron alloy) inside a coil of wire carrying an electric current. The electricity in the current produces a magnetic field. The strength of the magnet is directly proportional to the strength of the current and the number of coils of wire. Its polarity depends on the direction of flow of current. While the current flows, the core behaves like a magnet. However, as soon as the current stops, the core is demagnetized.

INTRODUCTION

Before going on to understand a magnetic circuit we must first understand what is meant by a magnetic field. Now you surely know that if you keep a magnet on the table and place a small iron object near it, it simply goes and sticks to the magnet. The force with which the piece is pulled decreases as its distance from the magnet increases. This phenomenon can be explained if you consider that the space around the magnet is permeated with a type of force which influences the iron piece near it. This force field is known as the magnetic field which can be visualized to be in the form of magnetic lines of flux. These are just imagine lines and do not exist actually but can only be experienced. The figure below shows these imaginary lines of magnetic flux surrounding a magnet.
Lines of Magnetic Force

Features of Lines of Flux
There are several characteristics of lines of force which are as follows.
Direction: any line of flux always points towards the north seeking pole of a magnet provided it is not under the influence of another magnetic medium except the magnetic
Closed Line: all lines of flux form a closed loop which emerge from the North Pole into the South Pole of the magnet
Independent Region: lines of flux never intersect each other.
Repulsion: lines of flux which are in the same direction always repel each other.

The Magnetic Circuit

The above discussion about magnetic field and lines of flux now leads us to the definition of a magnetic circuit. A magnetic circuit can be described as a complete closed path followed by any group of lines of magnetic flux. A magnetic circuit is quite similar to an electrical circuit in terms of various parameters which are associated with the magnetic circuit, some of which are described as follows.
Magneto-motive Force: just as electromotive force or emf makes electric current flow, similarly magneto-motive force or mmf makes the magnetic flux possible in a magnetic circuit. The units of mmf are ampere-turns, where turns signify the number of electric coil turns which is generating that mmf. Since number of terms is a dimensionless quantity, effectively the units of mmf are same as that of current, namely amperes.
Magnetic Field Strength: it refers to the mmf that exists per unit length of a magnetic circuit provided the circuit is homogeneous and of a uniform cross sectional area. In the earlier days it was also known as magnetizing force but this term is obsolete now. The units of magnetic field strength are amperes/meter.
Of course these are just a few basic concepts associated with a magnetic circuit. We will learn more about this subject in different articles as well.

magnetic circuit is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting offerromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators,transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.
The concept of a "magnetic circuit" exploits a one-to-one correspondence between the equations of the magnetic field in a non-hysteretic material to that of an electrical circuit. Using this concept the magnetic fields of complex devices such as transformers can be quickly solved using the methods and techniques developed for electrical circuits.
Some examples of magnetic circuits are: * horseshoe magnet with iron keeper (low-reluctance circuit) * horseshoe magnet with no keeper (high-reluctance circuit) * electric motor (variable-reluctance circuit)

EMF drives a current of electrical charge in electrical circuits, magnetomotive force (MMF) 'drives' magnetic flux through magnetic circuits. The term 'magnetomotive force', though, is a misnomer since it is not a force nor is anything moving. It is perhaps better to call it simply MMF. In analogy to the definition of EMF, the magnetomotive force around a closed loop is defined as:

The MMF represents the potential that a hypothetical magnetic charge would gain by completing the loop. The magnetic flux that is driven is not a current of magnetic charge; it merely has the same relationship to MMF that electric current has to EMF. (See microscopic origins of reluctance below for a further description.)
The unit of magnetomotive force is the ampere-turn (At), represented by a steady, direct electric current of one ampere flowing in a single-turn loop of electrically conducting material in a vacuum. The gilbert (Gi), established by the IEC in 1930 [1], is the CGS unit of magnetomotive force and is a slightly smaller unit than the ampere-turn. The unit is named after William Gilbert (1544–1603) English physician and natural philosopher.

The magnetomotive force can often be quickly calculated using Ampere's law. For example, the magnetomotive force of long coil is:
,
where N is the number of turns and I is the current in the coil. In practice this equation is used for the MMF of real inductors with N being the winding number of the inducting coil.
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Magnetic flux An applied MMF 'drives' magnetic flux through the magnetic components of the system. The magnetic flux through a magnetic component is proportional to the number of magnetic field lines that pass through the cross sectional area of that component. This is the net number, i.e. the number passing through in one direction, minus the number passing through in the other direction. The direction of the magnetic field vector B is by definition from the south to the north pole of a magnet inside the magnet; outside the field lines go from north to south.
The flux through an element of area perpendicular to the direction of magnetic field is given by the product of the magnetic field and the area element. More generally, magnetic flux Φ is defined by a scalar product of the magnetic field and the area element vector. Quantitatively, the magnetic flux through a surface S is defined as the integral of the magnetic field over the area of the surface

For a magnetic component the area S used to calculate the magnetic flux Φ is usually chosen to be the cross-sectional area of the component.
The SI unit of magnetic flux is the weber (in derived units: volt-seconds), and the unit of magnetic field is the weber per square meter, or tesla.

CONCEPT AND LAWS OF ANALOGY

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Hopkinson's law: the magnetic analogy to Ohm's law
In electronic circuits, Ohm's law is an empirical relation between the EMF applied across an element and the current I it generates through that element. It is written as:

where R is the electrical resistance of that material. Hopkinson's law is a counterpart to Ohm's law used in magnetic circuits. The law is named after the British electrical engineer, John Hopkinson. It states that[1][2]

where is the magnetomotive force (MMF) across a magnetic element, φ is the magnetic flux through the magnetic element, and is the magnetic reluctance of that element. (It shall be shown later that this relationship is due to the empirical relationship between the H-field and the magnetic field B,B=μH, where μ is the permeability of the material.) Like Ohm's law, Hopkinson's law can be interpreted either as an empirical equation that works for some materials, or it may serve as a definition of reluctance.
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Reluctance Magnetic reluctance, or magnetic resistance, is analogous to resistance in an electrical circuit (although it does not dissipate magnetic energy). In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. It is a scalar, extensive quantity, akin to electrical resistance.
The total reluctance is equal to the ratio of the (MMF) in a passive magnetic circuit and the magnetic flux in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux. (see phasors)
The definition can be expressed as:

where is the reluctance in ampere-turns per weber (a unit that is equivalent to turns per henry).
Magnetic flux always forms a closed loop, as described by Maxwell's equations, but the path of the loop depends on the reluctance of the surrounding materials. It is concentrated around the path of least reluctance. Air and vacuum have high reluctance, while easily magnetized materials such as soft iron have low reluctance. The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force(pull).
The inverse of reluctance is called permeance.

Its SI derived unit is the henry (the same as the unit of inductance, although the two concepts are distinct).

The reluctance of a magnetically uniform magnetic circuit element can be calculated as:

where l is the length of the element in metres μ = μrμ0 is the permeability of the material ( μr is the relative permeability of the material (dimensionless), and μ0 is the permeability of free space)
A is the cross-sectional area of the circuit in square metres
This is similar to the equation for electrical resistance in materials, with permeability being analogous to conductivity; the reciprocal of the permeability is known as magnetic reluctivity and is analogous to resistivity. Longer, thinner geometries with low permeabilities lead to higher reluctance. Low reluctance, like low resistance in electric circuits, is generally preferred.[citation needed]
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Summary of analogy between magnetic circuits and electrical circuits
The following table summarizes the mathematical analogy between electrical circuit theory and magnetic circuit theory. This is mathematical analogy and not a physical one. Objects in the same row have the same mathematical role; the physics of the two theories are very different. For example, current is the flow of electrical charge, while magnetic flux is not the flow of any quantity.

Analogy between 'magnetic circuits' and electrical circuits | Magnetic equivalent | Symbol | Units | Electric equivalent | Symbol | Magnetomotive force (MMF) | | ampere-turn | Definition of EMF | | H-field | H | ampere/meter | Electric field | E | Magnetic flux | φ | weber | Electric Current | I | Hopkinson's Law | | | Ohm's Law | | Reluctance | | 1/Henry | Electrical resistance | R | Permanence | | Henry | Electric conductance | unit: Siemens | relation between B and H | | | Microscopic Ohm's Law | | Magnetic field B | B | tesla | Current density | J | permeability | μ | Henry/meter | Electrical conductivity | σ |
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Limitations of the analogy
When using the analogy between magnetic circuits and electric circuits, the limitations of this analogy must be kept in mind. Electric and magnetic circuits are only superficially similar because of the similarity between Hopkinson's law and Ohm's law. Magnetic circuits have significant differences, which must be taken into account in their construction: * Electric currents represent the flow of particles (electrons) and carry power, which is dissipated as heat in resistances. Magnetic fields don't represent the "flow" of anything, and no power is dissipated in reluctances. * The current in typical electric circuits is confined to the circuit, with very little "leakage". In typical magnetic circuits not all of the magnetic field is confined to the magnetic circuit; there is significant "leakage flux" in the space outside the magnetic cores, which must be taken into account but is difficult to calculate. * Most importantly, magnetic circuits are nonlinear; the reluctance in a magnetic circuit is not constant, as resistance is, but varies depending on the magnetic field. At high magnetic fluxes the ferromagnetic materials used for the cores of magnetic circuits saturate, limiting the magnetic flux, so above this level the reluctance increases rapidly. The reluctance also increases at low fluxes. In addition, ferromagnetic materials suffer from hysteresis so the flux in them depends not just on the instantaneous MMF but also on the past history of MMF. After the source of the magnetic flux is turned off,remanent magnetism is left in ferromagnetic circuits, creating a flux with no MMF.
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Circuit Laws

Magnetic circuit
Magnetic circuits obey other laws that are similar to electrical circuit laws. For example, the total reluctance of reluctances in series is:

This also follows from Ampère's law and is analogous to Kirchhoff's voltage law for adding resistances in series. Also, the sum of magnetic fluxes into any node is always zero:

This follows from Gauss's law and is analogous to Kirchhoff's current law for analyzing electrical circuits.
Together, the three laws above form a complete system for analysing magnetic circuits, in a manner similar to electric circuits. Comparing the two types of circuits shows that: * The equivalent to resistance R is the reluctance Rm * The equivalent to current I is the magnetic flux Φ * The equivalent to voltage V is the magnetomotive Force F
Magnetic circuits can be solved for the flux in each branch by application of the magnetic equivalent of Kirchhoff's Voltage Law (KVL) for pure source/resistance circuits. Specifically, whereas KVL states that the voltage excitation applied to a loop is equal to the sum of the voltage drops (resistance times current) around the loop, the magnetic analogue states that the magnetomotive force (achieved from ampere-turn excitation) is equal to the sum of MMF drops (product of flux and reluctance) across the rest of the loop. (If there are multiple loops, the current in each branch can be solved through a matrix equation—much as a matrix solution for mesh circuit branch currents is obtained in loop analysis—after which the individual branch currents are obtained by adding and/or subtracting the constituent loop currents as indicated by the adopted sign convention and loop orientations.) PerAmpère's law, the excitation is the product of the current and the number of complete loops made and is measured in ampere-turns. Stated more generally:

(Note that, per Stokes's theorem, the closed line integral of H dot dl around a contour is equal to the open surface integral of curl H dot dA across the surface bounded by the closed contour. Since, from Maxwell's equations, curl H = J, the closed line integral of H dot dl evaluates to the total current passing through the surface. This is equal to the excitation, NI, which also measures current passing through the surface, thereby verifying that the net current flow through a surface is zero ampere-turns in a closed system that conserves energy.)
More complex magnetic systems, where the flux is not confined to a simple loop, must be analysed from first principles by using Maxwell's equations.

Analogies between magnetic circuits and electrical circuits are easy to be made: * The magnetic flux which flows through a magnetic circuit, corresponds to the electrical current / which flows through an electrical circuit; * the magnetomotive force F, corresponds to the electromotive force U; * reluctance R of a magnetic conductor by lenght, S section and permeability, corresponds to resistance R of an electrical conductor by lenght, Ssection and conductivity; we can write R = şi R = ; * finally Hopkison's Law F = R. corresponds to Ohm's Law U = R.I.
We can also define the permeance of a magnetic circuit P = 1/R, which corresponds to G = 1/R conductance of an electrical circuit. Magnetic circuit | Electrical circuit | Flux () | Current (I) | Magnetomotive force(F) | Electromotive force (U) | Reluctance (R) | Resistance (R) | Permeance (P) | Conductance (G) | | | Hopkison's Law (F = R.) | Ohm's Law (U = R.I) |
Analogy magnetic circuits / electrical circuits

Equivalent magnet circuit
The analysis through the finite element method allows us to check the pertinency of the hypothesis, according to which the flux travels, mainly, through the ferromagnetic castings and the three air-gap portions. Between two consecutive equiflux curves presented in figure 4, always travels the same quantity of magnetic flux.
The hypothesis we considered, is reduced, in fact, to the dereliction of the leakage flux (the one that does not travel the air-gap), a flux which gets smaller as the size of the air-gap that must be traveled gets smaller or as the relative permeability of the ferromagnetic material gets higher. 2.
LAWS OF CIRCUIT

Hopkins law of magnet circuit

If Ri şi Re have similar values (meaning that the whirls are smaller than the medium radius Rm = (Ri+Re)/2), we can consider, without risking major errors, that all the integration contours situated within the torus have the approximately same Rmlenght.
From here - the magnetic induction is constant in any point of a right section of the torus. As induction is, in any point, perpendicularly to the right section (because it is tangential to the in tegration contour), the  flux through a right sectoin of the torus can be approximated: | (4) | where S is the right section of the torus.
Combining equations (2) and (4) the result will be | (5) | with = 2..Rm
By noting and defining: * F = N.I magnetomotive force expressed in ampere-turns; * R = , reluctance of the magnetic circuit, thus (5) could be write in this form: | (6) |
This ecuation is also known as The Hopkinson's Law

Application
Magnetic levitation train, Maglev, is a system in which the train runs levitated from the guideway (track) by using electromagnetic forces between superconducting magnets on board the train and coils on the guideway. The acceleration and braking system of the train are also handled by using electromagnets. The frictionless motion offered by magnetic levitation provides an extremely smooth, quite, and fast ride with speeds in excess of 500 km/h. Maglev is considered as a relatively cheap and fast transportation alternative to conventional rail trains, cars or airplanes.

Due to the symmetry, on the chosen integration contours, the induction field produced by / current that flows through the reel is always tangential at contour and has constant amplitude. The result is: * If the contour has the radius R1 smaller than Ri (the internal radial of the annular core) - the 1 contour from figure 2) 1: | (1) | * If the contour has the radius R2 bigger than Ri but smaller than Re (the external radius of the annular core) the 2 contour from figure 2): | (2) | * finally, if the contour has the R3 bigger than Re - the 3 contour from figure 2): | (3) | where 0 represents the magnetic permeability of the vacuum and of the air, and  represents the magnetic permeability of the material from which the annular core is made.
It is ascertained that in any point outside the torus, the field is null. The entire flux induced by the current, circulates, therefore, within this volume, similar to an electrical circuit in which the power only flows through conductors. By analogy, we can define torus as being a magnetic circuit.

Reference
Google. com 1. SHeaviside O., Electrical Papers. Vol.2. - L.; N.Y.: Macmillan, 1892, p. 166. 2. Joule J., Scientific Papers, vol. 1. - 1884, p. 36.