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 A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core, and thus a varying magnetic field through the secondary winding. This varying magnetic can be quickly solved using the methods and techniques developed for electrical circuits.
A magnetic circuit is made up of one or more closed paths containing a magnetic flux Magnetic flux (Greek letter Φ ), is a measure of the magnetic field strength existing on a two dimensional surface, such as one side of a magnet. In textbook diagrams, magnetic flux is usually pictured as cluster of vectors attached to a geometrically abstract surface. Each vector intersects a separate point on the surface. The SI unit of. It generally contains magnetic Magnetism is a category of behaviour of materials that respond at an atomic or subatomic level to an applied magnetic field. For example, the most well known form of magnetism is ferromagnetism such that some ferromagnetic materials produce their own persistent magnetic field. However, all materials are influenced to greater or lesser degree by elements such as permanent magnets A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials and attracts or repels other magnets, ferromagnetic Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. Ferromagnetism is the strongest type; it is the only type that can produce forces strong enough to be felt, and is responsible for the common phenomena of materials, and electromagnets An electromagnet is a type of magnet whose magnetic field is produced by the flow of electric current. The magnetic field disappears when the current ceases, but may also contain air gaps and other materials.
Some examples of magnetic circuits are:
- horseshoe A horseshoe is a U-shaped item made of metal or of modern synthetic materials, nailed or glued to the hooves of horses and some other draught animals. Like a shoe on a human, it is used to protect the animal's feet from wear and tear. Professional horseshoers, also called farriers or blacksmiths , attach horseshoes on the palmar surface of the magnet A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials like iron and attracts or repels other magnets with iron keeper (low-reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating magnetic energy it stores magnetic energy. In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magnetic circuit)
- horseshoe magnet with no keeper (high-reluctance circuit)
- electric motor An electric motor uses electrical energy to produce mechanical energy, very typically through the interaction of magnetic fields and current-carrying conductors. The reverse process, producing electrical energy from mechanical energy, is accomplished by a generator or dynamo. Many types of electric motors can be run as generators, and vice versa (variable-reluctance circuit)
Magnetomotive force (MMF)
Similar to the way, that EMF More formally, emf is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals. The electric potential difference is created by separating positive and negative charges, thereby generating an electric field. The created electrical potential difference drives current flow if a 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 More formally, emf is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals. The electric potential difference is created by separating positive and negative charges, thereby generating an electric field. The created electrical potential difference drives current flow if a, the magnetomotive force around a closed loop is defined as:
The MMF represents the potential that a hypothetical magnetic charge A magnetic monopole is a hypothetical particle in physics that is a magnet with only one pole . In more technical terms, it would have a net "magnetic charge". Modern interest in the concept stems from particle theories, notably the grand unification theory and superstring theories, which predict their existence 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 electrical 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 Electric current means, depending on the context, a flow of electric charge or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both of one ampere The ampere is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. In practice, its name is often shortened to amp flowing in a single-turn loop of electrically conducting material in a vacuum In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". Even putting aside the complexities of the quantum vacuum, the classical notion of a perfect vacuum with gaseous pressure of exactly. The gilbert (Gi), established by the IEC The International Electrotechnical Commission is a non-profit, non-governmental international standards organization that prepares and publishes International Standards for all electrical, electronic and related technologies – collectively known as "electrotechnology". IEC standards cover a vast range of technologies from power in 1930 [1], is the CGS The centimetre-gram-second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism unit of magnetomotive force and is a slightly smaller unit than the ampere-turn. The unit is named after William Gilbert William Gilbert, also known as Gilbard, was an English physician and natural philosopher. He was an early Copernican, and passionately rejected both the prevailing Aristotelian philosophy and the Scholastic method of university teaching. He is remembered today largely for his book De Magnete (1601), and is credited as one of the originators of the (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 In mathematics, the winding number of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point. The winding number depends on the orientation of the curve, and is negative if the curve travels around the point clockwise of the inducting coil.
Magnetic flux
Main article: magnetic flux Magnetic flux (Greek letter Φ ), is a measure of the magnetic field strength existing on a two dimensional surface, such as one side of a magnet. In textbook diagrams, magnetic flux is usually pictured as cluster of vectors attached to a geometrically abstract surface. Each vector intersects a separate point on the surface. The SI unit ofAn applied MMF 'drives' magnetic flux Magnetic flux (Greek letter Φ ), is a measure of the magnetic field strength existing on a two dimensional surface, such as one side of a magnet. In textbook diagrams, magnetic flux is usually pictured as cluster of vectors attached to a geometrically abstract surface. Each vector intersects a separate point on the surface. The SI unit of through the magnetic components of the system. The magnetic flux through a magnetic component is proportional to the number of magnetic field lines Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field 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 One could argue, based on the work of James Clerk Maxwell, that the transport definition precedes the more recent way the term is used in electromagnetism. The specific quote from Maxwell is "In the case of fluxes, we have to take the integral, over a surface, of the flux through every element of the surface. The result of this operation is through an element of area Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3-dimensional solid is the total area of the exposed surface, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of perpendicular In geometry, two lines or planes , are considered perpendicular (or orthogonal) to each other if they form congruent adjacent angles (a T-shape). The term may be used as a noun or adjective. Thus, referring to Figure 1, the line AB is the perpendicular to CD through the point B. Note that by definition, a line is infinitely long, and strictly to the direction of magnetic field is given by the product of the magnetic field Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field and the area Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3-dimensional solid is the total area of the exposed surface, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of element. More generally, magnetic flux Φ is defined by a scalar product In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the dot that is often used to designate this operation; the alternative name scalar product emphasizes the scalar of the magnetic field and the area element vector. Quantitatively, the magnetic flux through a surface S is defined as the integral Integration is an important concept in mathematics and, together with differentiation, is one of the two main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite 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 The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science unit A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement of magnetic flux is the weber In physics, the weber is the SI unit of magnetic flux. A flux density of one Wb/m2 (one weber per square meter) is one tesla (in derived units: volt-seconds), and the unit of magnetic field is the weber per square meter, or tesla The tesla is the SI derived unit of magnetic field B (which is also known as "magnetic flux density" and "magnetic induction"). One tesla is equal to one weber per square meter, and it was defined in 1960 in honor of the Yugoslavian-American inventor, physicist, and electrical engineer Nikola Tesla. One billionth of a tesla is.
Hopkinson's law: the magnetic analogy to Ohm's law
In electronic circuits An electronic circuit is composed of individual electronic components, such as resistors, transistors, capacitors, inductors, and diodes, connected by conductive wires or traces through which electrical current can flow. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified,, Ohm's law In electrical circuits, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them, provided that the temperature remains constant is an empirical relation between the EMF More formally, emf is the external work expended per unit of charge to produce an electric potential difference across two open-circuited terminals. The electric potential difference is created by separating positive and negative charges, thereby generating an electric field. The created electrical potential difference drives current flow if a applied across an element and the current Electric current means, depending on the context, a flow of electric charge or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both I it generates through that element. It is written as:
where R is the electrical resistance The electrical resistance of an object is a measure of its attraction to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material of that material. Hopkinson's law is a counterpart to Ohm's law In electrical circuits, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them, provided that the temperature remains constant used in magnetic circuits. The law is named after the British electrical engineer Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of engineering that deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and, John Hopkinson. It states that[1][2]
where is the magnetomotive force (MMF) across a magnetic element, φ is the magnetic flux Magnetic flux (Greek letter Φ ), is a measure of the magnetic field strength existing on a two dimensional surface, such as one side of a magnet. In textbook diagrams, magnetic flux is usually pictured as cluster of vectors attached to a geometrically abstract surface. Each vector intersects a separate point on the surface. The SI unit of 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 In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. Magnetic permeability is typically represented by the Greek letter μ. The term was coined in September, 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity of the material.) Like Ohm's law, Hopkinson's law can be interpreted either as an emperical equation that works for some materials, or it may serve as a definition of reluctance.
Reluctance
Main article: Reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is analogous to resistance in an electrical circuit, but rather than dissipating magnetic energy it stores magnetic energy. In likeness to the way an electric field causes an electric current to follow the path of least resistance, a magneticMagnetic reluctance, or magnetic resistance, is analogous to resistance The electrical resistance of an object is a measure of its attraction to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material in an electrical Electricity is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning and static electricity, but in addition, less familiar concepts, such as the electromagnetic field and electromagnetic induction circuit An electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches (although it does not dissipate magnetic energy). In likeness to the way an electric field In physics, an electric field is a property that describes the space that surrounds electrically charged particles or that which is in the presence of a time-varying magnetic field. This electric field exerts a force on other electrically charged objects. The concept of an electric field was introduced by Michael Faraday causes an electric current Electric current means, depending on the context, a flow of electric charge or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both to follow the path of least resistance, a magnetic field Magnetic fields surround magnetic materials and electric currents and are detected by the force they exert on other magnetic materials and moving electric charges. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector 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).
Microscopic origins of reluctance
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]
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.
| 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 | Henry | Electrical resistance | R | |
| relation between B and H | Microscopic Ohm's Law | |||
| Magnetic field B | B | tesla | Current density | J |
| permeability | μ | Henry/meter | Electrical conductivity | σ |
|
