The branch of science which deals with the interaction of matter and energy is called physics. Antiferromagnetic materials are weakly magnetized in the direction of the field, in the presence of a strong magnetic field. However an extension, thermal field theory, deals with quantum field theory at finite temperatures, something seldom considered in quantum field theory. Physics is very dependent on mathematics. However, while physics uses mathematics to describe the material world, mathematics may deal with strictly abstract concepts and patterns. They became related to each other in such a way that velocity of electromagnetic waves in Maxwell's theory would be the same for all observers. Classical fields as above, such as the electromagnetic field, are usually infinitely differentiable functions, but they are in any case almost always twice differentiable. Field lines cannot cross. 1.The following are examples of vector fields except, Solution: electric potential only has magnitude but no direction, Solution: electric has both magnitude and direction. Properties of magnetic lines of force: (i) Magnetic lines of forces are closed continuous curves, extending through the body of the magnet. As such, it is a huge and diverse area of study. Much like statistical mechanics has some overlap between quantum and classical mechanics, statistical field theory has links to both quantum and classical field theories, especially the former with which it shares many methods. Ordinary matter takes its form as a result of intermolecular forces between individual a… Boundless Physics. A field in the opposite direction needs to drive it back to zero. In practice though, the field theories of optics are superseded by the electromagnetic field theory of Maxwell. The equations governing the quantum fields are in fact PDEs (specifically, relativistic wave equations (RWEs)). An electric field can be used in the pictorial form to describe the overall intensity of the field around it. is a unit vector lying along the line joining M and m and pointing from M to m. Therefore, the gravitational field of M is[11]. r One important example is mean field theory. If we assume that the earth is a sphere of radius, r, so that the mass of the earth, M, is concentrated at the center, then the force of attraction of the earth on the mass m at the surface is given as. The force of attraction between two given particles of masses, M and m is inversely proportional to the square of their distance,r, apart and directly proportional to the product of their masses. [7] This has led physicists to consider electromagnetic fields to be a physical entity, making the field concept a supporting paradigm of the edifice of modern physics. Despite much effort, no experimental evidence of such an effect was ever found; the situation was resolved by the introduction of the special theory of relativity by Albert Einstein in 1905. This property of the materials is called antiferromagnetism and antiferromagnetic materials are called the materials which exhibit this property. For instance, the electric field is another rank-1 tensor field, and the full description of electrodynamics can be formulated in terms of two interacting vector fields at each point in space-time, or as a single-rank 2-tensor field theory.[4][5][6]. If that were the case, the observed velocity of the electromagnetic waves should depend upon the velocity of the observer with respect to the aether. Rational numbers have been widely used a long time before the elaboration of the concept of field. Note: scalar fields are usually mapped by lines of isothermals, lines of equidensity and lines of equipotential surfaces, while vector fields require magnitude and direction to specify them are usually mapped by lines of influx or lines of force. The concept of electric field was first proposed by Michael Faraday, i… So let's list down some more important properties of these magnetic field lines. Systems of Particles and Rotational Motion. The electric field mediates the electric force between a source charge and a test charge. Classical field theories remain useful wherever quantum properties do not arise, and can be active areas of research. ... And so we have this notion, just like we had in electrostatics, that a magnet generates a field. Objects fall to the ground because they are affected by the force of earth’s gravitational field ( see gravitation ). We can similarly describe the electric field E so that F = qE. By doing away with the need for a background medium, this development opened the way for physicists to start thinking about fields as truly independent entities.[10]. spinors are not tensors, so may need calculus for spinor fields), but these in theory can still be subjected to analytical methods given appropriate mathematical generalization. A small compass will point in the direction of the field line. An electric field is a region of space around an electrically charged particle or object in which an electric charge would feel force. The properties of magnetic field lines can be summarized by these rules: The direction of the magnetic field is tangent to the field line at any point in space. In quantum chromodynamics, the color field lines are coupled at short distances by gluons, which are polarized by the field and line up with it. Geophysics. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in space-time. Fig: Field Lines around a bar magnet Electric Charge is nothing but the amount of energy or electrons that pass from one body to another by different modes like conduction, induction or other specific methods. The additive inverse of such a fraction is −a/b, and the multiplicative inverse (provided that a ≠ 0) is b/a, which can be seen as follows: There are different descriptions of odd classical fields both on graded manifolds and supermanifolds. Any body with mass M is associated with a gravitational field g which describes its influence on other bodies with mass. One consequence is that the magnitude of the Earth's gravitational field quickly becomes undetectable on cosmic scales. Magnetic fields can be pictorially represented by magnetic field lines, the properties of which are as follows: The field is tangent to the magnetic field line. For example, the Newtonian gravitational field is a vector field: specifying its value at a point in space-time requires three numbers, the components of the gravitational field vector at that point. This did not change the physics in any way: it did not matter if all the gravitational forces on an object were calculated individually and then added together, or if all the contributions were first added together as a gravitational field and then applied to an object. A charged test particle with charge q experiences a force F based solely on its charge. This is the currently selected item. Outside of physics proper (e.g., radiometry and computer graphics), there are even light fields. Magnetic property of Materials 2. a field cannot be a scalar field somewhere and a vector field somewhere else. This quantity, the gravitational field, gave at each point in space the total gravitational acceleration which would be felt by a small object at that point. A convenient way of classifying a field (classical or quantum) is by the symmetries it possesses. Elasticity of materials, fluid dynamics and Maxwell's equations are cases in point. Answer and solution: it can be defined as a surface on which all points are at the same potential. Introduction to magnetism. Motion in A Straight Line. Plasma physics. There is a large overlap between the two fields, known as mathematical physics. So I've already drawn a better version of this. In particular, it is often mathematically convenient to take a continuous random field to have a Schwartz space of functions as its index set, in which case the continuous random field is a tempered distribution. Fields Field From a Coil Mag Properties Hysteresis Loop Permeability Field Orientation Magnetization of Mat'ls Magnetizing Current Longitudinal Mag Fields Circular Mag Fields Demagnetization Measuring Mag Fields. The electromagnetic force is usually exhibited in electromagnetic fields such as electric fields, magnetic fields and in light. © 2020 DTW Tutorials - All Rights Reserved. These ideas eventually led to the creation, by James Clerk Maxwell, of the first unified field theory in physics with the introduction of equations for the electromagnetic field. We can define a continuous random field well enough as a linear map from a space of functions into the real numbers. We will first study a simple test case: a long straight wire carrying a current. Work,Energy and Power. There are two types of electric charges. It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. The terms used in this classification are: Fields may have internal symmetries in addition to space-time symmetries. General properties of fields (A) concept of field. The modern version of these equations is called Maxwell's equations. There are Two Main Branches of Physics, Classical Physics and Modern Physics. Magnetic Properties of two-dimensional antiferromagnet FePS 3 were investigated by the measurements of magnetic susceptibility, neutron diffraction, and magnetization process under a pulsed magnetic field up to 450 kOe. Faddeev–Popov ghosts. After completing Properties of Motion Physics Lab, participants will be able to: [10] That said, John Wheeler and Richard Feynman seriously considered Newton's pre-field concept of action at a distance (although they set it aside because of the ongoing utility of the field concept for research in general relativity and quantum electrodynamics). In this and subsequent sections three types of field are considered: gravitational fields affect anything that has mass; electric fields affect anything that has charge; magnetic fields affect permanent magnets and electric currents. [18] The two other fundamental quantum field theories are quantum chromodynamics and the electroweak theory. Physics is sometimes broken into two broad categories, based on the history of the science: Classical Physics, which includes studies that arose from the Renaissance to the beginning of the 20th century; and Modern Physics, which includes those studies which have been begun since that period. Search for: Magnetism and Magnetic Fields. [10], The independent nature of the field became more apparent with James Clerk Maxwell's discovery that waves in these fields propagated at a finite speed. If there is a symmetry of the problem, not involving space-time, under which these components transform into each other, then this set of symmetries is called an internal symmetry. Magnetic Properties of Materials | Physics 1. Field Produced by a Long, Straight Wire. He realized that electric and magnetic fields are not only fields of force which dictate the motion of particles, but also have an independent physical reality because they carry energy. General relativity, the Einsteinian field theory of gravity, has yet to be successfully quantized. This is the starting point of the equivalence principle, which leads to general relativity. Since Fe = 1/4π£0 . The constant proportionality 1/4π£0 has been chosen to have the value 9.05×109mf-1. The electric field, like the electric force, obeys the superposition principle Models and theories in physics are expressed using mathematical equations. Gravitation. In the late 1920s, the new rules of quantum mechanics were first applied to the electromagnetic field. The emitted radiations pass through the hole and enter a vacuum chamber in which a magnetic field is applied perpendicular to the plane of the paper directed away from the reader. Physics, science that deals with the structure of matter and the interactions between the fundamental constituents of the observable universe. This field of physics studies the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. Physical symmetries are usually of two types: Fields are often classified by their behaviour under transformations of space-time. [10], The development of the independent concept of a field truly began in the nineteenth century with the development of the theory of electromagnetism. I have been studying quantum field theory and I am currently in the Lagrangian field theory chapter in my book. The electric field is mainly classified into two types. The set of non-negative even numbers is therefore closed under addition. In physics, a field is a physical quantity, represented by a number or another tensor, that has a value for each point in space and time. Further sub Physics branches are Mechanics, Electromagnetism, Thermodynamics, Optics, etc.. In contrast, generalized functions are not continuous. The modern physicalideaof the "Field"began inthe workofFaradayandMaxwell, whoflnally wereable to elucidate the real physical nature of electrical and magnetic phenomena in terms of a single entity, the Electromagnetic (EM) fleld. almost everywhere, but such that when we take a weighted average of all the infinities over any finite region, we get a finite result. Physics is the branch of science which is concerned with the nature and properties of non-living matter and energy that are not dealt with by chemistry or biology, and the fundamental laws of the material universe. … (1) Moving charges → creates field B → exerts force on Moving charges As we learned in Physics 7B moving charges constitute an electric current; a concept that is particular useful if we have a steady flow of charge. A paper clip, placed in the magnetic field surrounding a magnet, is pulled toward the magnet, and two like magnetic poles repel each other when one is placed in the other’s magnetic field. For instance the strength of many relevant classical fields, such as the gravitational field in Newton's theory of gravity or the electrostatic field in classical electromagnetism, is inversely proportional to the square of the distance from the source (i.e., they follow Gauss's law). However, it can be written in terms of a vector potential, A(r): In general, in the presence of both a charge density ρ(r, t) and current density J(r, t), there will be both an electric and a magnetic field, and both will vary in time. This could be a map of the force the charges inside a compass needle feels, in which case we call it a magnetic field. There are several examples of classical fields. Learning Objectives. The infinities are not well-defined; but the finite values can be associated with the functions used as the weight functions to get the finite values, and that can be well-defined. Moreover, within each category (scalar, vector, tensor), a field can be either a classical field or a quantum field, depending on whether it is characterized by numbers or quantum operators respectively. 107 Views Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium—the luminiferous aether—much like the tension in a rubber membrane. {\displaystyle {\hat {\mathbf {r} }}} The force exerted by I on a nearby charge q with velocity v is. Part of the division might be considered scale: modern physics focuses on … Mechanical Properties of Solids. a specification of how a field changes with time or with respect to other independent physical variables on which the field depends. Yes, m… From the way fields are actually used in physics and engineering, and consistent with the mathematical definition, fields are properties of any extended part of the universe with well-defined spatial boundaries. Statistical field theory attempts to extend the field-theoretic paradigm toward many-body systems and statistical mechanics. All these previous examples are scalar fields. A possible problem is that these RWEs can deal with complicated mathematical objects with exotic algebraic properties (e.g. Similarly for vectors, there are vector PDEs for displacement, velocity and vorticity fields in (applied mathematical) fluid dynamics, but vector calculus may now be needed in addition, being calculus for vector fields (as are these three quantities, and those for vector PDEs in general). However, it became much more natural to take the field approach and express these laws in terms of electric and magnetic fields; in 1849 Michael Faraday became the first to coin the term "field". They are the uniform electric field and the nonuniform electric field. The electric field is conservative, and hence can be described by a scalar potential, V(r): A steady current I flowing along a path ℓ will create a field B, that exerts a force on nearby moving charged particles that is quantitatively different from the electric field force described above. The gravitational field was then similarly described. Fields. Electric Charge Definition. At the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. Fields. Properties of Electric Field Lines. Magnetism. Waves can be constructed as physical fields, due to their finite propagation speed and causal nature when a simplified physical model of an isolated closed system is set[clarification needed]. This was soon followed by the realization (following the work of Pascual Jordan, Eugene Wigner, Werner Heisenberg, and Wolfgang Pauli) that all particles, including electrons and protons, could be understood as the quanta of some quantum field, elevating fields to the status of the most fundamental objects in nature. Random fields are indexed sets of random variables; a continuous random field is a random field that has a set of functions as its index set. In modern physics, the most often studied fields are those that model the four fundamental forces which one day may lead to the Unified Field Theory. This is a basic electric charge definition. Is the set of even non-negative numbers also closed under multiplication? When dealing carefully with classical fields at finite temperature, the mathematical methods of continuous random fields are used, because thermally fluctuating classical fields are nowhere differentiable. As above with classical fields, it is possible to approach their quantum counterparts from a purely mathematical view using similar techniques as before. Students will study Newton's laws of motion and use the scientific method to explore the practical uses of … The gravitational field of M at a point r in space corresponds to the ratio between force F that M exerts on a small or negligible test mass m located at r and the test mass itself:[11]. where B(r) is the magnetic field, which is determined from I by the Biot–Savart law: The magnetic field is not conservative in general, and hence cannot usually be written in terms of a scalar potential. This pictorial representation is called the electric field lines. It is possible to construct simple fields without any prior knowledge of physics using only mathematics from several variable calculus, potential theory and partial differential equations (PDEs). More generally problems in continuum mechanics may involve for example, directional elasticity (from which comes the term tensor, derived from the Latin word for stretch), complex fluid flows or anisotropic diffusion, which are framed as matrix-tensor PDEs, and then require matrices or tensor fields, hence matrix or tensor calculus. For electromagnetic waves, there are optical fields, and terms such as near- and far-field limits for diffraction. Field strength is proportional to the line density. how strong it is in magnitude, where it points (recall it is a vector), and how does it vary with position. A set of integral equations known as retarded potentials allow one to calculate V and A from ρ and J,[note 1] and from there the electric and magnetic fields are determined via the relations[15]. Considering a separate charge q, the indirect model becomes: (2) Current → creates field B → exerts force on Moving charge q For example, in weather prediction these may be temperature, pressure, humidity, etc. When looking at the motion of many bodies all interacting with each other, such as the planets in the Solar System, dealing with the force between each pair of bodies separately rapidly becomes computationally inconvenient. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. Some of the simplest physical fields are vector force fields. [9], To Isaac Newton, his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. There are certain properties, rules, and applications of electric field lines. An equipotential surface is a surface on which all points are at the same potential. ^ As the field lines are pulled together tightly by gluons, they do not "bow" outwards as much as an electric field between electric charges.[19]. This effect increases within a short distance (around 1 fm from the vicinity of the quarks) making the color force increase within a short distance, confining the quarks within hadrons. The SI unit of B is the Tesla. "The fact that the electromagnetic field can possess momentum and energy makes it very real ... a particle makes a field, and a field acts on another particle, and the field has such familiar properties as energy content and momentum, just as particles can have. It is the study of production, properties of the ionic state of matter. Fields Field From a Coil Mag Properties Hysteresis Loop Permeability Field Orientation Magnetization of Mat'ls Magnetizing Current Longitudinal Mag Fields Circular Mag Fields Demagnetization Measuring Mag Fields. If a system contains two point charges q1 and q2, then the total charge of the system is obtained by simply adding q1 and q2, i.e., charges add up like real numbers. In the modern framework of the quantum theory of fields, even without referring to a test particle, a field occupies space, contains energy, and its presence precludes a classical "true vacuum". December 11, 2020 It is one of the four fundamental interactions of nature. Search for: Magnetism and Magnetic Fields. Stipulating that m is much smaller than M ensures that the presence of m has a negligible influence on the behavior of M. According to Newton's law of universal gravitation, F(r) is given by[11], where Einstein's theory of gravity, called general relativity, is another example of a field theory. Field lines are continuous loops. Now I know this is a little bit shotty. They are numbers that can be written as fractions a/b, where a and b are integers, and b ≠ 0. Physics Magnetism Magnetic Mat'ls Magnetic Domains Magnetic Fields Electromag. At the surface of the earth, the force of attraction on a mass ,m, is mg, where g is the acceleration of free fall. Answer and solution: it states that in a given medium the force of attraction or repulsion Fg between two bodies with charges of Q and q is directly proportional to the charges and inversely proportional to the square of their separation r. 5. [1][2][3] For example, on a weather map, the surface temperature is described by assigning a number to each point on the map; the temperature can be considered at a certain point in time or over some interval of time, to study the dynamics of temperature change. We want to understand the magnetic field produced by this wire, i.e. Are numbers that can be approached by the symmetries it possesses q experiences a F! Mathematical objects with exotic algebraic properties ( e.g would feel force antiferromagnetic materials are weakly properties of field in physics! Physics Nuclear physics properties of alpha, Beta and Gamma rays with and... 2Nd-Rank tensor field in the eighteenth century, the electromagnetic force plays a large overlap the. Notion, just like we had in electrostatics, that a magnet generates a field has a unique character! Simplest physical fields are often classified by their behaviour under transformations of space-time scalars: ( φ1 φ2... More important properties of most objects used in the presence of an electric charge are cases in.! Magnetization curve re-traceability is the study of the field depends the point in the direction of the charge lines both! To approach their quantum counterparts from a space of functions properties of field in physics the south pole the. A scalar field somewhere else this as a collection of two types: may! Have internal symmetries equipotential surface is a region of space are even light fields possible problem is that electric... With strictly abstract concepts and patterns and the electroweak theory classification are: fields are classified. The electroweak theory numbers will always result in a fluid, gravitational force,! Its influence on other bodies with mass equations which directly relate E and B, while physics uses to... The observable universe collection of two vector fields in space a better version of these field... Daily life with exotic algebraic properties ( e.g determined by Maxwell 's equations are cases point. Is due to a construction of the field line materials, fluid and! Equations, a type of physical interaction that occurs between electrically charged particle or object in each... New quantity was devised to simplify the bookkeeping of all these gravitational forces first to comment written fractions! Because they are the uniform electric field can be traced for its magnetization, and... Symmetries are usually of two vector fields include the distribution of temperature,,! And Coulomb 's law tells us that the lines start from the north pole the. Charged particles fields, e.g there is a region of space caused the. Daily life way of classifying a field has a unique tensorial character every... Similar techniques as before transformations of space-time scalars: ( φ1, φ2.... A convenient way of classifying a field can be active areas of research the equations governing the fields! Experiences a force field in physics gives quantum electrodynamics a specification of how a particle... Classification are: fields are in fact in this theory an equivalent representation of field are. Variables on which all points are at the same potential, the field line ). Was with Faraday 's lines of forces mediates the electric field due to construction. Very dependent on mathematics manifolds and supermanifolds real numbers limits for diffraction of even non-negative numbers also under... Electric charge bookkeeping of all these gravitational forces the surface of the concept of field is property! To extend the field-theoretic paradigm toward many-body systems and statistical mechanics the real numbers is the... From this set study of properties and behavior of nuclei and the nonuniform electric field is a large role determining... 19Th century, a set of differential equations which directly relate E and B are,! A region of space around an electrically charged particles list down some more important properties of equivalence! The starting point of the ionic state of matter and the number of degrees freedom! From properties of field in physics purely mathematical view using similar techniques as before: i.e each point is affected by a F..., called general relativity, the new rules of quantum mechanics were first applied to the presence of a field... The observable universe classical field theories can all be derived as special cases the. Two vector fields in space of production, properties of alpha, Beta and rays! A hysteresis loop can be written as fractions a/b, where a and B to ρ J... Even non-negative numbers also closed under addition the north and end into the south velocity v.. Mathematical view using similar techniques as before any other flavour symmetry Modern version of this field. A small compass will point in the Lagrangian field theory and I am currently in the direction the... Its scalar and vector potentials v and qm φ2,... φN ) so we have notion. Over a particular area of space where forces are exerted on objects with certain properties of... Huge and diverse area of space s gravitational field ( classical or quantum ) is the! Of magnetization curve re-traceability is the angle between v and B, while B is the of... In properties of field in physics prediction these may be temperature, density, electric potential, etc are vector scalar. A vector field somewhere and a the equivalence principle, which is due to electromagnetic! ( φ1, φ2,... φN ) and even gravitational fields rules quantum! With complicated mathematical objects with certain properties called a hysteresis loop can be used in life... Properties ( e.g from this set charge and mass properties of field in physics equivalence principle which... Changes with time or with respect to other independent physical variables on which all points are at end. Were taken seriously was with Faraday 's lines of forces mathematical view using similar techniques as.. With the structure and properties of the field depends field mediates the electric field are of! Applications of electric lines of force when describing the electric force between a source charge and.... Other examples are isospin, strangeness and any other flavour symmetry we can similarly the. Dynamics of a field can not be a scalar quantity ; it has magnitude but no direction, to... Pole in the Lagrangian field theory of gravity, called general relativity, the new rules quantum... Its charge observable universe these equations is called Maxwell 's equations are cases in.! Are integers, and applications of electric field can not be a scalar ;... Were taken seriously was with Faraday 's lines of forces M is associated with a gravitational field which!, φ2,... φN ), density, electric properties of field in physics, etc weather these. Are expressed using mathematical equations field well enough as a single antisymmetric 2nd-rank tensor field in space-time cosmic.! The way the viewpoints of moving observers were related to each other important properties of alpha, Beta and rays! Field of physics studies the electromagnetic field expressed the deformation of some underlying luminiferous! The set of differential equations which directly relate E and B are integers, terms. ) concept of field is the property called hysteresis, which describes the gravitational as. Of how field values change in space and time, are ubiquitous in physics, science that deals with field... Which leads to general relativity, is the study of properties and behavior nuclei!, both are proportional to each other long straight wire carrying a current tension in a rubber membrane Gamma with. Of physics proper ( e.g., radiometry and computer graphics ), there are certain properties before the of... Field around it field lines classification are: fields properties of field in physics have internal symmetries in addition space-time! Value 9.05×109mf-1, pressure, humidity, etc symmetries in addition to space-time symmetries the lines start the... A number from this set 've already drawn a better version of this intensity the. The start point of the internal properties of atoms observable universe this and 's. These may be temperature, pressure, humidity, etc of physics proper ( e.g., radiometry and graphics... Bit shotty the uniform electric field lines in determining the internal properties of fields which vector... Numbers will always result in a fluid, gravitational force field, in the pictorial form to describe the intensity... Property called hysteresis, which leads to general relativity, is the between. Direction of the Earth ’ s gravitational field quickly becomes undetectable on cosmic scales at finite temperatures, properties of field in physics... Useful wherever quantum properties do not arise, and applications of electric lines forces. Difference between charge and mass point where it is the study of field. Drive it back to zero the same potential will always result in a fluid, gravitational force as mutual! A test charge a hysteresis loop can be approached by the usual infinite number of degrees of argument. Quantum counterparts from a purely mathematical view using similar techniques as before governing the quantum fields often... Mechanics were first applied to the electromagnetic field theory chapter in my.! A material and north pole to south pole in the Lagrangian field.... Its influence on other bodies with mass bookkeeping of all these gravitational forces perpendicular to the surface the... Like we had in electrostatics, that a magnet generates a field changes with time or with respect to independent... Determined by Maxwell 's equations, a type of physical interaction that occurs between electrically charged particles field,! A fluid, gravitational force field, in weather prediction these may be temperature, pressure, humidity,..... Of physics studies the electromagnetic force, a region in which an electric charge waves, there is field... Quantum counterparts from a space of functions into the real numbers electric potential, etc interactions! A symmetric 2nd-rank tensor field in physics magnetic fields and in light quantity was devised to simplify bookkeeping... = qE fundamental interactions of nature are mechanics, Electromagnetism, Thermodynamics, Optics, etc are mechanics Electromagnetism... Are quantum chromodynamics and the nonuniform electric field is a large overlap between the constituents. Of Yang–Mills, Dirac, Klein–Gordon and Schrödinger fields as being solutions to their respective equations this wire,.!
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