Laws of electromagnetism | Article about Laws of electromagnetism by The Free Dictionary Laws of electromagnetism | Article about Laws of electromagnetism by The Free Dictionary Also found in: Dictionary , Thesaurus , Wikipedia . Maxwell's equations Four differential equations proposed by James Clerk Maxwell in 1864 as the basis of the theory of electromagnetic waves. They may be written, in vector notation, as Eqs. (1)–(4), where D is the electric (1) (3) (4) displacement, B the magnetic flux density, E the electric field strength or intensity, H the magnetic field strength or intensity, ρ the charge density, and i the current density. The first equation states that electric flux lines, if they end at all, will do so on electric charges. The second states that magnetic flux lines never terminate. The third is a form of Faraday's law of induction, which states that the rate of change of the magnetic flux threading a circuit equals the electromotive force or line integral of E around the circuit. The fourth integral is based partially on A. M.

Ampère's experiments on steady currents which show that the line integral of the magnetic intensity H (or B /μ, where μ is the permeability) around a closed curve equals the current encircled. See Displacement current Maxwell’s Equations the fundamental equations of classical macroscopic electrodynamics that describe electromagnetic phenomena in any medium. The equations were formulated by J. C. Maxwell in the 1860’s on the basis of a generalization of the empirical laws of electric and magnetic phenomena. By using these laws as a basis and developing M. Faraday’s productive idea that the interactions between electrically charged bodies take place through an electromagnetic field, Maxwell created the theory of electromagnetic processes, which is expressed mathematically by Maxwell’s equations. The present form of the equations was given by the German physicist H. Hertz and the British physicist O. Heaviside. Maxwell’s equations relate the quantities that characterize an electromagnetic field to its sources, that is, to the spatial distribution of electric charges and currents. In a vacuum, the electromagnetic field is characterized by two vector quantities that are dependent on spatial coordinates and on time—the electric field intensity E and magnetic induction B.

These quantities determine the forces that act because of the field on the charges and currents whose distribution in space is given by the charge density ρ (the charge per unit volume) and the current density j (the charge passing in unit time through unit area perpendicular to the direction of motion of the charges). In addition to the vectors E and B, auxiliary vector quantities that are dependent on the state and properties of the medium—the electric displacement D and the magnetic field intensity H—are introduced to describe electromagnetic processes in a material medium (matter). Maxwell’s equations make it possible to determine the fundamental characteristics of a field (E, B, D, and H) at each point in space at any moment if the field sources j and ρ are known as functions of the coordinates and of time. The equations can be written in integral or differential form [below they are given in the absolute (Gaussian) system of units].

Maxwell’s equations in integral form determine on the basis of given charges and currents not the field vectors E, B, D and H themselves at different points in space but certain integral quantities that depend on the distribution of these field characteristics: the line integral (circulation) of the vectors E and H around any closed curve and the surface integral (flux) of the vectors D and B through any closed surface. Maxwell’s first equation is a generalization for variable fields of the empirical law of Ampere which deals with the excitation of a magnetic field by an electric current. Maxwell advanced the hypothesis that magnetic fields are generated not only by currents flowing in conductors but also by varying electric fields in dielectrics or a vacuum. A quantity proportional to the rate of change of the electric field with time was called displacement current by Maxwell. A displacement current excites a magnetic field by the same law as does a conduction current (this was confirmed later experimentally). The total current, which is equal to the sum of the conduction current and the displacement current, is always closed.

Maxwell’s first equation has the form: that is, the line integral of the magnetic field vector around a closed curve L (the sum of the scalar products of the vector H at a given point in the circuit and an infinitesimal segment dl of the curve) is given by the total current through any surface S bounded by the curve. Here jn is the projection of the conduction current density j on the normal to the infinitesimal area ds, which is a part of the surface S; (1/4π)(∂Dn/∂t) is the projection of the displacement current density on the same normal; and c = 3 × 1010 cm/sec is a constant equal to the rate of propagation of electromagnetic interactions in a vacuum. Maxwell’s second equation is a mathematical formulation of Faraday’s law of elecromagnetic induction and is written in the form that is, the line integral of the electric field vector along a closed curve L (the electromotive force of induction) is given by the rate of change of the magnetic induction through the surface S bounded by the curve.

Here Bn is the projection of the magnetic induction vector B on the normal to the area ds; the minus sign corresponds to the Lenz law for the direction of an induced current. Maxwell’s third equation expresses the experimental findings on the absence of magnetic charges analogous to electric charges (a magnetic field is produced only by currents): that is, the magnetic induction through any closed surface S is equal to zero. Maxwell’s fourth equation, which is usually called Gauss’ theorem, is a generalization of the law of interaction of stationary electric charges — Coulomb’s law: that is, the electric flux through an arbitrary closed surface S is determined by the electric charge located within this surface (in the volume V bounded by the given surface).

If we assume that the vectors of an electromagnetic field (E, B, D, H) are continuous functions of the coordinates, then, by considering the line integrals of the vectors H and E around infinitesimal closed curves and the surface integrals of the vectors B and D through surfaces that bound infinitesimal volumes, we can proceed from the integral relations (1a)-(1d) to a system of differential equations that are valid at any point in space, that is, we can obtain a differential form of Maxwell’s equations (which is usually more convenient for solving problems): Here curl and div are the differential operators known as curl and divergence, which act on the vectors H, E, B, and D. The physical import of equations (2) is the same as that of equations (1a)-(1d). Maxwell’s equations in form (1a)-(1d) or (2) do not form a complete closed system that would allow calculation of electromagnetic processes in the presence of a material medium. They must be supplemented by relations between the vectors E, H, D, B, and j, which are not independent.

The relations among these vectors are determined by the properties and state of the medium; D and j are expressed in terms of E, and B is expressed in terms of H: (3) D = D(E), B = B(H), j = j(E) These three equations are called the constitutive relations, or the material equations; they describe the electromagnetic properties of the medium and have a definite form for a specific medium. In a vacuum, D ≡ E and B ≡ H. The set of field equations (2) and constitutive relations (3) forms the complete system of equations. Maxwell’s macroscopic equations describe a medium phenomenologically, without examining the complex mechanism of the interaction of the electromagnetic field with the charged particles of the medium. Maxwell’s equations can be obtained from the Lorentz-Maxwell equations for microscopic fields and for specific conceptions of the structure of matter by averaging the microfields over small space-time intervals. The basic field equations (2) and the specific form of the constitutive relations (3) are obtained in this manner, and the form of the field equations is independent of the properties of the medium.

The constitutive relations are very complex in the general case, since the vectors D, B, and j at a given point in space and a given moment may depend on the fields E and H at all points in the medium and at all previous moments of time. In some media the vectors D and B may be nonzero with E and H equal to zero (ferroelectrics and ferromagnetics). However, for the majority of isotropic media and up to extremely large fields, the equations of state have the simple linear form (4) D = εE, B = μH, j = σE + jnon Here, ε(x,y,z) is the dielectric constant and μ(x,y,z) is the permeability of the medium, which characterize its electric and magnetic properties, respectively (in the selected system of units ε = μ = 1 for a vacuum); the quantity σ(x,y,z) is called the specific electric conductivity; and jnon is the density of nonelectromagnetic currents, that is, currents maintained by any forces other than those of an electric field (such as a magnetic field or diffusion).

In Maxwell’s phenomenological theory, the macroscopic characteristics ε, μ, and σ of the electromagnetic properties of the medium must be found experimentally. In the Lorentz-Maxwell microscopic theory they can be calculated. The dielectric constant ε and permeability μ actually determine the contribution to the electromagnetic field by bound charges, which are part of the electrically neutral atoms and molecules of matter. The experimental determination of ε, μ, and σ makes it possible to calculate the electromagnetic field in a medium without solving the difficult auxiliary problem of the distribution of bound charges and of the corresponding currents in the substance. In Maxwell’s equations the charge density ρ and the current density j are the densities of free charges and currents, and the auxiliary vectors H and D are introduced such that the circulation of the vector H is determined only by the motion of free charges, and the flux of vector D by the density of the distribution of these charges in space. If the electromagnetic field is considered in two adjacent media, then the field vectors at their interface may experience discontinuities.

In this case, equations (2) must be supplemented by the boundary conditions Here jsur and σ are the densities of the surface current and charge, the brackets and parentheses represent, respectively, the vector and scalar products of the vectors, n is the unit vector along the normal to the interface in the direction of the second medium from the first (1 → 2), and the subscripts refer to the different sides of the interface. The basic field equations (2) are linear, while the material equations (3) may also be nonlinear. Nonlinear effects are usually observed in quite strong fields. In linear media [satisfying relations (4)] and, in particular, in a vacuum, Maxwell’s equations are linear and thus the principle of superposition is valid: when the fields are superimposed they do not affect each other. A number of laws of conservation stem from Maxwell’s equations. In particular, we can derive from equations (1a) and (1d) the relation (called the equation of continuity) which is the law of conservation of electric charge: the total current flowing through any closed surface S per unit time is equal to the rate of change of the charge within the volume V bounded by this surface.

If there is no current through the surface, then the charge in the volume remains unchanged. It follows from Maxwell’s equations that an electromagnetic field has energy and momentum. The energy density w (the energy per unit volume of the field) is equal to Electromagnetic energy can travel in space. The energy flux density is given by the Poynting vector The direction of the Poynting vector is perpendicular to both E and H and coincides with the direction of propagation of the electromagnetic energy, and its magnitude is equal to the energy passing per unit time through unit area of surface perpendicular to the vector P. If no conversions of electromagnetic energy into other forms take place, then, according to Maxwell’s equations, the change in energy in any volume per unit time is equal to the flux of electromagnetic energy through the surface that bounds this volume. If heat is released within the volume at the expense of electromagnetic energy, then the law of conservation of energy is written in the form where Q is the quantity of heat released per unit time. The density of electromagnetic field momentum g (the momentum per unit volume of a field) is related to the energy flux density by the expression The existence of electromagnetic field momentum was first detected by P. N.

Lebedev in experiments on the measurement of the pressure of light (1899). As can be seen from (7), (8), and (10), an electromagnetic field always has energy, but the energy flux and electromagnetic momentum are nonzero only when both electric and magnetic fields exist simultaneously (and these fields are not parallel to each other). Maxwell’s equations lead to the fundamental conclusion of the finiteness of the speed of propagation of electromagnetic interactions (equal to c = 3 × 1010 cm/sec). This means that when the charge or flux density changes at some point in space, the electromagnetic field that it generates does not change at the point of observation at the same moment but rather after a time τ = R/c, where R is the distance from the element of current or charge to the point of observation. The existence of electromagnetic waves, of which light waves are a particular case (as Maxwell first demonstrated), is possible because of the finite rate of propagation of electromagnetic interactions. Electromagnetic phenomena take place in the same way in all inertial frames of reference, that is, they satisfy the principle of relativity.

Accordingly, Maxwell’s equations do not change their form in going over from one inertial frame of reference to another (they are relativistically invariant). Satisfaction of the principle of relativity for electromagnetic processes proved to be incompatible with classical concepts of space and time. The required revision of these concepts led to the creation of the special theory of relativity (A. Einstein, 1905). The form of Maxwell’s equations remains unchanged in going over to a new inertial frame of reference if the spatial coordinates, time, the field vectors E, H, B, and D, current density j, and charge density ρ change in accordance with the Lorentz transformation (which expresses new, relativistic concepts of space and time). The relativistically invariant form of Maxwell’s equations underscores the fact that electric and magnetic fields form a unified whole. Maxwell’s equations describe an enormous range of phenomena. They underlie electric and radio technology and play a very important role in the development of such significant areas of modern physics as plasma physics, the problem of controlled thermonuclear reactions, magnetohydrodynamics, nonlinear optics, the design of charged-particle accelerators, and astrophysics.

Maxwell’s equations are inapplicable only for electromagnetic waves of high frequencies, when quantum effects become significant, that is, when the energy of the individual quanta of the electromagnetic field—photons—is large and a comparatively small number of photons take part in the processes. REFERENCES Faraday Law of Electromagnetic Induction | Electrical4u Faraday Law of Electromagnetic Induction Next » In 1831, Michael Faraday, an English physicist gave one of the most basic laws of electromagnetism called Faraday's law of electromagnetic induction. This law explains the working principle of most of the electrical motors , generators, electrical transformers and inductors . This law shows the relationship between electric circuit and magnetic field . Faraday performs an experiment with a magnet and coil. During this experiment, he found how emf is induced in the coil when flux linked with it changes. He has also done experiments in electro-chemistry and electrolysis . Faraday's Experiment RELATIONSHIP BETWEEN INDUCED EMF AND FLUX In this experiment, Faraday takes a magnet and a coil and connects a galvanometer across the coil.

At starting, the magnet is at rest, so there is no deflection in the galvanometer i.e needle of galvanometer is at the center or zero position. When the magnet is moved towards the coil, the needle of galvanometer deflects in one direction. When the magnet is held stationary at that position, the needle of galvanometer returns back to zero position. Now when the magnet is moved away from the coil, there is some deflection in the needle but in opposite direction and again when the magnet becomes stationary, at that point with respect to coil, the needle of the galvanometer returns back to the zero position. Similarly, if magnet is held stationary and the coil is moved away and towards the magnet, the galvanometer shows deflection in similar manner. It is also seen that, the faster the change in the magnetic field, the greater will be the induced emf or voltage in the coil.

Position of magnet Magnet moves away from the coil Deflection in galvanometer but in opposite direction Magnet is held stationary at same position (away from the coil) No deflection in galvanometer Conclusion: From this experiment, Faraday concluded that whenever there is relative motion between conductor and a magnetic field, the flux linkage with a coil changes and this change in flux induces a voltage across a coil. Michael Faraday formulated two laws on the basis of above experiments. These laws are called Faraday's laws of electromagnetic induction. Faraday's Laws Faraday's First Law Any change in the magnetic field of a coil of wire will cause an emf to be induced in the coil. This emf induced is called induced emf and if the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current. Method to change magnetic field: By moving a magnet towards or away from the coil By moving the coil into or out of the magnetic field. By changing the area of a coil placed in the magnetic field By rotating the coil relative to the magnet. Faraday's Second Law It states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil.

The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil. Faraday Law Formula Consider a magnet approaching towards a coil. Here we consider two instants at time T1 and time T2. Flux linkage with the coil at time, T1 = NΦ1 Wb Flux linkage with the coil at time, T2 = NΦ2 wb Change in flux linkage = N(Φ2 - Φ1) Let this change in flux linkage be, Φ = Φ2 - Φ1 So, the Change in flux linkage = NΦ Now the rate of change of flux linkage = NΦ / t Take derivative on right hand side we will get The rate of change of flux linkage = NdΦ/dt But according to Faraday's law of electromagnetic induction, the rate of change of flux linkage is equal to induced emf. Considering Lenz's Law .

Where, flux Φ in Wb = B.A B = magnetic field strength A = area of the coil HOW TO INCREASE EMF INDUCED IN A COIL By increasing the number of turns in the coil i.e N- From the formulae derived above it is easily seen that if number of turns of coil is increased, the induced emf also gets increased. By increasing magnetic field strength i.e B surrounding the coil- Mathematically if magnetic field increases, flux increases and if flux increases emf induced will also get increased. Theoretically, if the coil is passed through a stronger magnetic field, there will be more lines of force for coil to cut and hence there will be more emf induced. By increasing the speed of the relative motion between the coil and the magnet - If the relative speed between the coil and magnet is increased from its previous value, the coil will cut the lines of flux at a faster rate, so more induced emf would be produced. Applications of Faraday Law Faraday law is one of the most basic and important laws of electromagnetism. This law finds its application in most of the electrical machines, industries and medical field etc.

Electrical Transformers It is a static ac device which is used to either step up or step down voltage or current. It is used in generating station, transmission and distribution system. The transformer works on Faraday's law. Electrical Generators The basic working principle of electrical generator is Faraday's law of mutual induction. Electric generator is used to convert mechanical energy into electrical energy. Induction Cookers The Induction cooker, is a most fastest way of cooking. It also works on principle of mutual induction. When current flows through the coil of copper wire placed below a cooking container, it produces a changing magnetic field. This alternating or changing magnetic field induces an emf and hence the current in the conductive container, and we know that flow of current always produces heat in it. Electromagnetic Flow Meters It is used to measure velocity of blood and certain fluids. When a magnetic field is applied to electrically insulated pipe in which conducting fluids are flowing, then according to Faraday's law, an electromotive force is induced in it. This induced emf is proportional to velocity of fluid flowing . Form the bases of Electromagnetic Theory Faraday's idea of lines of force is used in well known Maxwell's equations.

According to Faraday's law, change in magnetic field gives rise to change in electric field and the converse of this is used in Maxwell's equations. Musical Instruments It is also used in musical instruments like electric guitar, electric violin etc. Video Presentation of Faraday's Law Faraday's law (electromagnetism) - encyclopedia article - Citizendium Faraday's law (electromagnetism) This editable Main Article is under development and not meant to be cited; by editing it you can help to improve it towards a future approved , citable version. These unapproved articles are subject to a disclaimer . [ edit intro ] In physics , in particular in the theory of electromagnetism , Faraday's law of induction states that a change in magnetic flux generates an electromotive force (EMF, voltage difference). The law is named after the English scientist Michael Faraday , who discovered in 1831 on basis of observations that a change in a magnetic field induces an electric current. This is the phenomenon of electromagnetic induction. Some thirty years after Faraday's discovery, between 1861 and 1864, the Scottish mathematical physicist James Clerk Maxwell formulated the mathematical expression relating the change in magnetic flux to the induced EMF.

This relationship, known as Faraday's law of induction (to distinguish it from Faraday's laws of electrolysis), states that the EMF induced in a circuit is proportional to the rate of decrease of the magnetic flux that cuts across the circuit. By Ohm's law an EMF induces an electric current in a conductor. When one rotates a circuit in a static homogeneous magnetic field, the magnetic flux cutting across the circuit is changed. Hence this rotation generates an electric current in the circuit, which means that the work done by rotating the circuit inside a magnetic field is converted into an electric current. Thus, Faraday's law is the theoretical basis of the dynamo and the electric generator . Contents Faraday's law of electromagnetic induction relates the electromotive force [1] (EMF) to the time derivative of the magnetic flux Φ. The law reads where k = 1 for SI units and one over c (the speed of light) for Gaussian units . The EMF is defined as where the electric field E is integrated around a closed path C.

The magnetic flux Φ through a surface S that has C as boundary is defined as the surface integral, where dS is a vector normal (perpendicular) to the infinitesimal surface element dS and dS is of length dS. The dot stands for the inner product between the magnetic induction B and dS. In vacuum the magnetic induction B is proportional to the magnetic field H. (In SI units: B = μ0 H with μ0 the magnetic constant of the vacuum; in Gaussian units: B = H.) If, in the definition of the EMF, C is a conducting loop, then under influence of the EMF a current iind will run through it. The minus sign in Faraday's law has the consequence that the magnetic field generated by iind opposes the change in Φ; this phenomenon is known as Lenz' law . If the surface S is constant in size and direction, a change in Φ is solely due to a change in B. The magnetic flux can be varied by changing the angle between the field and surface.

For the simple case of a planar loop bordering a constant area A, and a homogeneous field B of strength B, the flux is given by where is a unit vector normal (perpendicular) to the plane S bordered by the loop. The initial condition α(0) = 0° is applied. Clearly, the flux is maximum, Φ(0), if α = 0°, i.e., if B is perpendicular to S. In the perpendicular case all of B passes through the surface. When B is parallel to surface, α = 90°, then there is no flux through the surface, Φ = 0, because B only grazes the surface. When α(t) becomes a function of time by rotation of the loop, Faraday's law shows that an EMF is induced of the form, When the rotation is uniform, i.e., α(t) linear in time t, it follows that the EMF has a sine dependence on time and an alternating current will be induced. CC Image Magnetic flux. The flux through surface S1 (yellow) is equal to the flux through surface S2 (gray). Both surfaces have the contour C (red) as boundary.

The flux through two surfaces that together form a closed surface is equal because of Gauss' law . Indeed, in the figure on the right the surfaces S1 and S2, which have the boundary C in common, form together a closed surface. Hence Gauss' law states that where the minus sign of the first term is due to the fact that the flux is into the volume enveloped by the two surfaces. It follows that and that the magnetic flux Φ can be computed with respect to any surface that has C as boundary. Connection to Maxwell's equation Application of Stokes' theorem gives where S is a surface that has C as boundary. From rewriting Faraday's law as follows, and the fact that S is arbitrary, we may conclude which is one of Maxwell's equations . Recall that k = 1 for SI units and k = 1/c for Gaussian units. Connection to Lorentz force CC Image Conducting bar moves to the right on conducting rails in homogeneous field B. Surface grows with v. Lorentz force is downward and gives an electric current iind in clockwise direction around the closed circuit. It is instructive to derive Faraday's law from the Lorentz force for a special case.

To that end an experimental setup is depicted in the figure on the right. A conducting bar of length a moves in positive x direction over two parallel pairs of conducting rails. The speed v of the bar is constant. The whole setup is placed in a homogeneous magnetic field B = μ0 H (we are using SI units) that points toward the reader, i.e., in positive z-direction. Homogeneity means that everywhere in the plane of drawing a magnetic field B of the same strength points toward the reader (parallel to the z-axis). The magnetic field is constant, but the surface S increases linearly in time The vector B points in positive z-direction and so does the normal to S, The time-dependence of the growing flux is solely due to the time-dependence of the growth of the surface. The time derivative of the magnetic flux in the figure is positive and equal to The Lorentz force (in SI units) is the cross product , where ey is a unit vector along the y-axis.

In order to obtain the electromotive force (EMF) one must integrate the inner product of electric force with path, FLor⋅dl, counter-clockwise around the circuit consisting of: the moving bar, the two pairs of unmoving rails and the unmoving conductor containing the ampmeter. The integration is counter-clockwise because of the right-hand screw rule applied to the direction of B. Except for the moving bar, where the force is constant and non-zero, there is no force in the circuit. The constant force acts over the length a of the moving bar and gives an EMF equal to force times path length, From equations (1) and (2) follows which indeed is Faraday's law of magnetic induction. The EMF gives a current iind in the direction of the Lorentz force, i.e., in a clockwise direction in the plane of drawing (the x-y plane). By Biot-Savart's law a current gives a circular magnetic field. The current iind has a tangent vector in the x-y plane that is in negative z-direction. Hence Bind opposes B, in accordance with Lenz' law .

Note ↑ The term EMF has historical origin, but is somewhat unfortunate as it is not a force but a potential. Faraday's Law's of Electromagnetic Induction - First law, Second Law Faraday's law's of Electromagnetic induction In 1831, Micheal Faraday formulated two laws on the bases of experiments. These laws are called Faraday's laws of electromagnetic induction. FIRST LAW First Law of Faraday's Electromagnetic Induction state that whenever a conductor are placed in a varying magnetic field emf are induced which is called induced emf, if the conductor circuit are closed current are also induced which is called induced current. Or Whenever a conductor is rotated in magnetic field emf is induced which are induced emf. SECOND LAW Second Law of Faraday's Electromagnetic Induction state that the induced emf is equal to the rate of change of flux linkages (flux linkages is the product of turns, n of the coil and the flux associated with it).

FARADAY'S LAW'S EXPLANATION KIRCHHOFF’S LAWS, ELECTROMAGNETIC INDUCTION, FARADAY'S LAW, LENZ’S LAW | Electromagnetic Induction | Inductance KIRCHHOFF’S LAWS, ELECTROMAGNETIC INDUCTION, FARADAY'S LAW, LENZ’S LAW KIRCHHOFF’S LAWS, ELECTROMAGNETIC INDUCTION, FARADAY'S LAW, LENZ’S LAW Copyright: Attribution Non-Commercial (BY-NC) KIRCHHOFF’S LAWS, ELECTROMAGNETIC INDUCTION, FARADAY'S LAW, LENZ’S LAW KIRCHHOFF’S LAWS Kirchhoff’s laws are basic analytical tools in order to obtain the solutions of currents and voltages for any electric circuit; whether it is supplied from a direct-current system or an alternating current system. Kirchhoff’s Current Law (KCL): KCL states that the algebraic sum of the current meeting at a point of junction iszero in any electrical network.

Simply the total current leaving the junction isequal to the total current entering to the junction.Towards junction = positive Away from junction = negative Kirchhoff’s Voltage Law (KVL): It states that in a closed circuit, the algebraic sum of all source voltages must beequal to the algebraic sum of all the voltage drops. Or sum of voltage dropsaround a closed loop will equal to the applied voltage. OHM'S LAW Ohm's law states that the current through a conductor between two points isdirectly proportional to the potential difference or voltage across the two points,and inversely proportional to the resistance between them.Ohm's Law defines the relationships between (P) power, (E) voltage, (I) current,and (R) resistance. One ohm is the resistance value through which one volt willmaintain a current of one ampere.The mathematical equation that describes this relationship is where V is the potential difference measured across the resistance in units of volts; I is the current through the resistance in units of amperes and R is the = Self Induction: When the e.m.f. is induced in the same circuit as that in whichthe current is changing, the property is called self inductance L.

Mutual inductance : The ability to produce a voltage in one circuit by varying acurrent in another.OR A varying current in the first or primary winding creates a varying magnetic fluxthrough the secondary winding. This varying magnetic field induces a varyingelectromotive force (EMF) or voltage in secondary winding.This effect is called mutual induction.Mutual inductance can be calculated using this formulae 21 LLKM += M = mutual inductanceK = co-efficient of couplingL1 = Self inductance of the primary L2= Self inductance of secondary 21 Electromagnetic theory | Article about Electromagnetic theory by The Free Dictionary Electromagnetic theory | Article about Electromagnetic theory by The Free Dictionary Related to Electromagnetic theory: electromagnetic theory of light , Maxwell's electromagnetic theory Maxwell's equations Four differential equations proposed by James Clerk Maxwell in 1864 as the basis of the theory of electromagnetic waves. They may be written, in vector notation, as Eqs.

(1)–(4), where D is the electric (1) (3) (4) displacement, B the magnetic flux density, E the electric field strength or intensity, H the magnetic field strength or intensity, ρ the charge density, and i the current density. The first equation states that electric flux lines, if they end at all, will do so on electric charges. The second states that magnetic flux lines never terminate. The third is a form of Faraday's law of induction, which states that the rate of change of the magnetic flux threading a circuit equals the electromotive force or line integral of E around the circuit. The fourth integral is based partially on A. M. Ampère's experiments on steady currents which show that the line integral of the magnetic intensity H (or B /μ, where μ is the permeability) around a closed curve equals the current encircled. See Displacement current Maxwell’s Equations the fundamental equations of classical macroscopic electrodynamics that describe electromagnetic phenomena in any medium. The equations were formulated by J. C. Maxwell in the 1860’s on the basis of a generalization of the empirical laws of electric and magnetic phenomena.

By using these laws as a basis and developing M. Faraday’s productive idea that the interactions between electrically charged bodies take place through an electromagnetic field, Maxwell created the theory of electromagnetic processes, which is expressed mathematically by Maxwell’s equations. The present form of the equations was given by the German physicist H. Hertz and the British physicist O. Heaviside. Maxwell’s equations relate the quantities that characterize an electromagnetic field to its sources, that is, to the spatial distribution of electric charges and currents. In a vacuum, the electromagnetic field is characterized by two vector quantities that are dependent on spatial coordinates and on time—the electric field intensity E and magnetic induction B. These quantities determine the forces that act because of the field on the charges and currents whose distribution in space is given by the charge density ρ (the charge per unit volume) and the current density j (the charge passing in unit time through unit area perpendicular to the direction of motion of the charges). In addition to the vectors E and B, auxiliary vector quantities that are dependent on the state and properties of the medium—the electric displacement D and the magnetic field intensity H—are introduced to describe electromagnetic processes in a material medium (matter).

Maxwell’s equations make it possible to determine the fundamental characteristics of a field (E, B, D, and H) at each point in space at any moment if the field sources j and ρ are known as functions of the coordinates and of time. The equations can be written in integral or differential form [below they are given in the absolute (Gaussian) system of units]. Maxwell’s equations in integral form determine on the basis of given charges and currents not the field vectors E, B, D and H themselves at different points in space but certain integral quantities that depend on the distribution of these field characteristics: the line integral (circulation) of the vectors E and H around any closed curve and the surface integral (flux) of the vectors D and B through any closed surface. Maxwell’s first equation is a generalization for variable fields of the empirical law of Ampere which deals with the excitation of a magnetic field by an electric current. Maxwell advanced the hypothesis that magnetic fields are generated not only by currents flowing in conductors but also by varying electric fields in dielectrics or a vacuum. A quantity proportional to the rate of change of the electric field with time was called displacement current by Maxwell.

A displacement current excites a magnetic field by the same law as does a conduction current (this was confirmed later experimentally). The total current, which is equal to the sum of the conduction current and the displacement current, is always closed. Maxwell’s first equation has the form: that is, the line integral of the magnetic field vector around a closed curve L (the sum of the scalar products of the vector H at a given point in the circuit and an infinitesimal segment dl of the curve) is given by the total current through any surface S bounded by the curve. Here jn is the projection of the conduction current density j on the normal to the infinitesimal area ds, which is a part of the surface S; (1/4π)(∂Dn/∂t) is the projection of the displacement current density on the same normal; and c = 3 × 1010 cm/sec is a constant equal to the rate of propagation of electromagnetic interactions in a vacuum.

Maxwell’s second equation is a mathematical formulation of Faraday’s law of elecromagnetic induction and is written in the form that is, the line integral of the electric field vector along a closed curve L (the electromotive force of induction) is given by the rate of change of the magnetic induction through the surface S bounded by the curve. Here Bn is the projection of the magnetic induction vector B on the normal to the area ds; the minus sign corresponds to the Lenz law for the direction of an induced current. Maxwell’s third equation expresses the experimental findings on the absence of magnetic charges analogous to electric charges (a magnetic field is produced only by currents): that is, the magnetic induction through any closed surface S is equal to zero. Maxwell’s fourth equation, which is usually called Gauss’ theorem, is a generalization of the law of interaction of stationary electric charges — Coulomb’s law: that is, the electric flux through an arbitrary closed surface S is determined by the electric charge located within this surface (in the volume V bounded by the given surface).

If we assume that the vectors of an electromagnetic field (E, B, D, H) are continuous functions of the coordinates, then, by considering the line integrals of the vectors H and E around infinitesimal closed curves and the surface integrals of the vectors B and D through surfaces that bound infinitesimal volumes, we can proceed from the integral relations (1a)-(1d) to a system of differential equations that are valid at any point in space, that is, we can obtain a differential form of Maxwell’s equations (which is usually more convenient for solving problems): Here curl and div are the differential operators known as curl and divergence, which act on the vectors H, E, B, and D. The physical import of equations (2) is the same as that of equations (1a)-(1d). Maxwell’s equations in form (1a)-(1d) or (2) do not form a complete closed system that would allow calculation of electromagnetic processes in the presence of a material medium. They must be supplemented by relations between the vectors E, H, D, B, and j, which are not independent.

The relations among these vectors are determined by the properties and state of the medium; D and j are expressed in terms of E, and B is expressed in terms of H: (3) D = D(E), B = B(H), j = j(E) These three equations are called the constitutive relations, or the material equations; they describe the electromagnetic properties of the medium and have a definite form for a specific medium. In a vacuum, D ≡ E and B ≡ H. The set of field equations (2) and constitutive relations (3) forms the complete system of equations. Maxwell’s macroscopic equations describe a medium phenomenologically, without examining the complex mechanism of the interaction of the electromagnetic field with the charged particles of the medium. Maxwell’s equations can be obtained from the Lorentz-Maxwell equations for microscopic fields and for specific conceptions of the structure of matter by averaging the microfields over small space-time intervals. The basic field equations (2) and the specific form of the constitutive relations (3) are obtained in this manner, and the form of the field equations is independent of the properties of the medium.

The constitutive relations are very complex in the general case, since the vectors D, B, and j at a given point in space and a given moment may depend on the fields E and H at all points in the medium and at all previous moments of time. In some media the vectors D and B may be nonzero with E and H equal to zero (ferroelectrics and ferromagnetics). However, for the majority of isotropic media and up to extremely large fields, the equations of state have the simple linear form (4) D = εE, B = μH, j = σE + jnon Here, ε(x,y,z) is the dielectric constant and μ(x,y,z) is the permeability of the medium, which characterize its electric and magnetic properties, respectively (in the selected system of units ε = μ = 1 for a vacuum); the quantity σ(x,y,z) is called the specific electric conductivity; and jnon is the density of nonelectromagnetic currents, that is, currents maintained by any forces other than those of an electric field (such as a magnetic field or diffusion).

In Maxwell’s phenomenological theory, the macroscopic characteristics ε, μ, and σ of the electromagnetic properties of the medium must be found experimentally. In the Lorentz-Maxwell microscopic theory they can be calculated. The dielectric constant ε and permeability μ actually determine the contribution to the electromagnetic field by bound charges, which are part of the electrically neutral atoms and molecules of matter. The experimental determination of ε, μ, and σ makes it possible to calculate the electromagnetic field in a medium without solving the difficult auxiliary problem of the distribution of bound charges and of the corresponding currents in the substance. In Maxwell’s equations the charge density ρ and the current density j are the densities of free charges and currents, and the auxiliary vectors H and D are introduced such that the circulation of the vector H is determined only by the motion of free charges, and the flux of vector D by the density of the distribution of these charges in space. If the electromagnetic field is considered in two adjacent media, then the field vectors at their interface may experience discontinuities.

In this case, equations (2) must be supplemented by the boundary conditions Here jsur and σ are the densities of the surface current and charge, the brackets and parentheses represent, respectively, the vector and scalar products of the vectors, n is the unit vector along the normal to the interface in the direction of the second medium from the first (1 → 2), and the subscripts refer to the different sides of the interface. The basic field equations (2) are linear, while the material equations (3) may also be nonlinear. Nonlinear effects are usually observed in quite strong fields. In linear media [satisfying relations (4)] and, in particular, in a vacuum, Maxwell’s equations are linear and thus the principle of superposition is valid: when the fields are superimposed they do not affect each other. A number of laws of conservation stem from Maxwell’s equations. In particular, we can derive from equations (1a) and (1d) the relation (called the equation of continuity) which is the law of conservation of electric charge: the total current flowing through any closed surface S per unit time is equal to the rate of change of the charge within the volume V bounded by this surface.

If there is no current through the surface, then the charge in the volume remains unchanged. It follows from Maxwell’s equations that an electromagnetic field has energy and momentum. The energy density w (the energy per unit volume of the field) is equal to Electromagnetic energy can travel in space. The energy flux density is given by the Poynting vector The direction of the Poynting vector is perpendicular to both E and H and coincides with the direction of propagation of the electromagnetic energy, and its magnitude is equal to the energy passing per unit time through unit area of surface perpendicular to the vector P. If no conversions of electromagnetic energy into other forms take place, then, according to Maxwell’s equations, the change in energy in any volume per unit time is equal to the flux of electromagnetic energy through the surface that bounds this volume. If heat is released within the volume at the expense of electromagnetic energy, then the law of conservation of energy is written in the form where Q is the quantity of heat released per unit time. The density of electromagnetic field momentum g (the momentum per unit volume of a field) is related to the energy flux density by the expression The existence of electromagnetic field momentum was first detected by P. N.

Lebedev in experiments on the measurement of the pressure of light (1899). As can be seen from (7), (8), and (10), an electromagnetic field always has energy, but the energy flux and electromagnetic momentum are nonzero only when both electric and magnetic fields exist simultaneously (and these fields are not parallel to each other). Maxwell’s equations lead to the fundamental conclusion of the finiteness of the speed of propagation of electromagnetic interactions (equal to c = 3 × 1010 cm/sec). This means that when the charge or flux density changes at some point in space, the electromagnetic field that it generates does not change at the point of observation at the same moment but rather after a time τ = R/c, where R is the distance from the element of current or charge to the point of observation. The existence of electromagnetic waves, of which light waves are a particular case (as Maxwell first demonstrated), is possible because of the finite rate of propagation of electromagnetic interactions. Electromagnetic phenomena take place in the same way in all inertial frames of reference, that is, they satisfy the principle of relativity.

Accordingly, Maxwell’s equations do not change their form in going over from one inertial frame of reference to another (they are relativistically invariant). Satisfaction of the principle of relativity for electromagnetic processes proved to be incompatible with classical concepts of space and time. The required revision of these concepts led to the creation of the special theory of relativity (A. Einstein, 1905). The form of Maxwell’s equations remains unchanged in going over to a new inertial frame of reference if the spatial coordinates, time, the field vectors E, H, B, and D, current density j, and charge density ρ change in accordance with the Lorentz transformation (which expresses new, relativistic concepts of space and time). The relativistically invariant form of Maxwell’s equations underscores the fact that electric and magnetic fields form a unified whole. Maxwell’s equations describe an enormous range of phenomena. They underlie electric and radio technology and play a very important role in the development of such significant areas of modern physics as plasma physics, the problem of controlled thermonuclear reactions, magnetohydrodynamics, nonlinear optics, the design of charged-particle accelerators, and astrophysics.

Maxwell’s equations are inapplicable only for electromagnetic waves of high frequencies, when quantum effects become significant, that is, when the energy of the individual quanta of the electromagnetic field—photons—is large and a comparatively small number of photons take part in the processes. REFERENCES electromagnetism | physics | Britannica.com Electromagnetism electricity Electromagnetism, science of charge and of the forces and fields associated with charge. Electricity and magnetism are two aspects of electromagnetism. Electricity and magnetism were long thought to be separate forces. It was not until the 19th century that they were finally treated as interrelated phenomena. In 1905 Albert Einstein ’s special theory of relativity established beyond a doubt that both are aspects of one common phenomenon. At a practical level, however, electric and magnetic forces behave quite differently and are described by different equations. Electric forces are produced by electric charges either at rest or in motion. Magnetic forces , on the other hand, are produced only by moving charges and act solely on charges in motion. Electric phenomena occur even in neutral matter because the forces act on the individual charged constituents .

The electric force in particular is responsible for most of the physical and chemical properties of atoms and molecules . It is enormously strong compared with gravity . For example, the absence of only one electron out of every billion molecules in two 70-kilogram (154-pound) persons standing two metres (two yards) apart would repel them with a 30,000-ton force . On a more familiar scale, electric phenomena are responsible for the lightning and thunder accompanying certain storms. Learn how the presence of electrons between two objects changes the notion of touch. © MinutePhysics (A Britannica Publishing Partner) Electric and magnetic forces can be detected in regions called electric and magnetic fields . These fields are fundamental in nature and can exist in space far from the charge or current that generated them. Remarkably, electric fields can produce magnetic fields and vice versa, independent of any external charge. A changing magnetic field produces an electric field, as the English physicist Michael Faraday discovered in work that forms the basis of electric power generation. Conversely, a changing electric field produces a magnetic field, as the Scottish physicist James Clerk Maxwell deduced. The mathematical equations formulated by Maxwell incorporated light and wave phenomena into electromagnetism.

He showed that electric and magnetic fields travel together through space as waves of electromagnetic radiation , with the changing fields mutually sustaining each other. Examples of electromagnetic waves traveling through space independent of matter are radio and television waves, microwaves , infrared rays , visible light , ultraviolet light , X-rays , and gamma rays . All of these waves travel at the same speed—namely, the velocity of light (roughly 300,000 kilometres, or 186,000 miles, per second). They differ from each other only in the frequency at which their electric and magnetic fields oscillate. Similar Topics velocity Maxwell’s equations still provide a complete and elegant description of electromagnetism down to, but not including, the subatomic scale. The interpretation of his work, however, was broadened in the 20th century. Einstein’s special relativity theory merged electric and magnetic fields into one common field and limited the velocity of all matter to the velocity of electromagnetic radiation. During the late 1960s, physicists discovered that other forces in nature have fields with a mathematical structure similar to that of the electromagnetic field .

These other forces are the strong force , responsible for the energy released in nuclear fusion , and the weak force , observed in the radioactive decay of unstable atomic nuclei. In particular, the weak and electromagnetic forces have been combined into a common force called the electroweak force. The goal of many physicists to unite all of the fundamental forces, including gravity, into one grand unified theory has not been attained to date. An important aspect of electromagnetism is the science of electricity, which is concerned with the behaviour of aggregates of charge, including the distribution of charge within matter and the motion of charge from place to place. Different types of materials are classified as either conductors or insulators on the basis of whether charges can move freely through their constituent matter. Electric current is the measure of the flow of charges; the laws governing currents in matter are important in technology, particularly in the production, distribution, and control of energy. Britannica Stories This article seeks to provide a qualitative understanding of electromagnetism as well as a quantitative appreciation for the magnitudes associated with electromagnetic phenomena. Fundamentals Everyday modern life is pervaded by electromagnetic phenomena.

When a lightbulb is switched on, a current flows through a thin filament in the bulb, and the current heats the filament to such a high temperature that it glows, illuminating its surroundings. Electric clocks and connections link simple devices of this kind into complex systems such as traffic lights that are timed and synchronized with the speed of vehicular flow. Radio and television sets receive information carried by electromagnetic waves traveling through space at the speed of light . To start an automobile , currents in an electric starter motor generate magnetic fields that rotate the motor shaft and drive engine pistons to compress an explosive mixture of gasoline and air; the spark initiating the combustion is an electric discharge, which makes up a momentary current flow. Coulomb’s law Many of these devices and phenomena are complex, but they derive from the same fundamental laws of electromagnetism. One of the most important of these is Coulomb’s law , which describes the electric force between charged objects. Formulated by the 18th-century French physicist Charles-Augustin de Coulomb , it is analogous to Newton’s law for the gravitational force. Both gravitational and electric forces decrease with the square of the distance between the objects, and both forces act along a line between them.

In Coulomb’s law, however, the magnitude and sign of the electric force are determined by the charge, rather than the mass, of an object. Thus, charge determines how electromagnetism influences the motion of charged objects. (Charge is a basic property of matter. Every constituent of matter has an electric charge with a value that can be positive, negative, or zero. For example, electrons are negatively charged, and atomic nuclei are positively charged. Most bulk matter has an equal amount of positive and negative charge and thus has zero net charge.) Connect with Britannica Eyjafjallajökull volcano The electric field from a charge is directed away from the charge when the charge is positive and toward the charge when it is negative. The electric field from a charge at rest is shown in Figure 1 for various locations in space. The arrows point in the direction of the electric field, and the length of the arrows indicates the strength of the field at the midpoint of the arrows. If a positive charge were placed in the electric field, it would feel a force in the direction of the field. A negative charge would feel a force in the direction opposite the direction of the field.

In calculations, it is often more convenient to deal directly with the electric field than with the charges. Frequently, more is known about the field than about the distribution of charges in space. For example, the distribution of charges in conductors is generally unknown because the charges move freely within the conductor. In static situations, however, the electric field in a conductor in equilibrium has a definite value, zero, because any force on the charges inside the conductor redistributes them until the field vanishes. The unit of electric field is newtons per coulomb, or volts per metre. The electric potential is another useful field. It provides an alternative to the electric field in electrostatics problems. The potential is easier to use, however, because it is a single number, a scalar, instead of a vector. The difference in potential between two places measures the degree to which charges are influenced to move from one place to another. If the potential is the same at two places (i.e., if the places have the same voltage ), charges will not be influenced to move from one place to the other. The potential on an object or at some point in space is measured in volts; it equals the electrostatic energy that a unit charge would have at that position.

In a typical 12-volt car battery , the battery terminal that is marked with a + sign is at a potential 12 volts greater than the potential of the terminal marked with the − sign. When a wire, such as the filament of a car headlight, is connected between the + and the − terminals of the battery, charges move through the filament as an electric current and heat the filament, and the hot filament radiates light. Magnetic fields and forces The magnetic force influences only those charges that are already in motion. It is transmitted by the magnetic field. Both magnetic fields and magnetic forces are more complicated than electric fields and electric forces. The magnetic field does not point along the direction of the source of the field; instead, it points in a perpendicular direction. In addition, the magnetic force acts in a direction that is perpendicular to the direction of the field. In comparison, both the electric force and the electric field point directly toward or away from the charge. The present discussion will deal with simple situations in which the magnetic field is produced by a current of charge in a wire . Certain materials, such as copper, silver, and aluminum, are conductors that allow charge to flow freely from place to place.

If an external influence establishes a current in a conductor, the current generates a magnetic field. For a long straight wire, the magnetic field has a direction that encircles the wire on a plane perpendicular to the wire. The strength of the magnetic field decreases with distance from the wire. The arrows in Figure 2 represent the size and direction of the magnetic field for a current moving in the direction indicated. Figure 2A shows an end view with the current coming toward the reader, while Figure 2B provides a three-dimensional view of the magnetic field at one position along the wire. In subsequent figures, continuous lines will be used to represent the direction of electric and magnetic fields. These lines emphasize the important fact that electric fields begin on positive charges and end on negative charges, while magnetic fields do not have beginnings or ends and close on themselves. The magnetic field shown in Figure 2 is unusually simple. Highly complex and useful magnetic fields can be generated by the proper choice of conductors to carry electric currents. Under development are thermonuclear fusion reactors for obtaining energy from the fusion of light nuclei in the form of very hot plasmas of hydrogen isotopes .

The plasmas have to be confined by magnetic fields (dubbed “magnetic bottles”) as no material container can withstand such high temperatures. Charged particles are also confined by magnetic fields in nature. Large numbers of charged particles, mostly protons and electrons, are trapped in huge bands around Earth by its magnetic field . These bands are known as the Van Allen radiation belts . Disturbance of Earth’s confining magnetic field produces spectacular displays, the so-called northern lights , in which trapped charged particles are freed and crash through the atmosphere to Earth. Interaction of a magnetic field with a charge How does the magnetic field interact with a charged object? If the charge is at rest, there is no interaction. If the charge moves, however, it is subjected to a force, the size of which increases in direct proportion with the velocity of the charge. The force has a direction that is perpendicular both to the direction of motion of the charge and to the direction of the magnetic field. There are two possible precisely opposite directions for such a force for a given direction of motion. This apparent ambiguity is resolved by the fact that one of the two directions applies to the force on a moving positive charge while the other direction applies to the force on a moving negative charge.

Figure 3 illustrates the directions of the magnetic force on positive charges and on negative charges as they move in a magnetic field that is perpendicular to the motion. Depending on the initial orientation of the particle velocity to the magnetic field, charges having a constant speed in a uniform magnetic field will follow a circular or helical path. Electric currents in wires are not the only source of magnetic fields. Naturally occurring minerals exhibit magnetic properties and have magnetic fields. These magnetic fields result from the motion of electrons in the atoms of the material. They also result from a property of electrons called the magnetic dipole moment, which is related to the intrinsic spin of individual electrons . In most materials, little or no field is observed outside the matter because of the random orientation of the various constituent atoms. In some materials such as iron , however, atoms within certain distances tend to become aligned in one particular direction. Magnets have numerous applications, ranging from use as toys and paper holders on home refrigerators to essential components in electric generators and machines that can accelerate particles to speeds approaching that of light. The practical application of magnetism in technology is greatly enhanced by using iron and other ferromagnetic materials with electric currents in devices like motors.

These materials amplify the magnetic field produced by the currents and thereby create more powerful fields. While electric and magnetic effects are well separated in many phenomena and applications, they are coupled closely together when there are rapid time fluctuations. Faraday’s law of induction describes how a time-varying magnetic field produces an electric field . Important practical applications include the electric generator and transformer . In a generator, the physical motion of a magnetic field produces electricity for power. In a transformer, electric power is converted from one voltage level to another by the magnetic field of one circuit inducing an electric current in another circuit. The existence of electromagnetic waves depends on the interaction between electric and magnetic fields. Maxwell postulated that a time-varying electric field produces a magnetic field. His theory predicted the existence of electromagnetic waves in which each time-varying field produces the other field. For example, radio waves are generated by electronic circuits known as oscillators that cause rapidly oscillating currents to flow in antennas ; the rapidly varying magnetic field has an associated varying electric field. The result is the emission of radio waves into space (see electromagnetic radiation: Generation of electromagnetic radiation ). Many electromagnetic devices can be described by circuits consisting of conductors and other elements.

These circuits may operate with a steady flow of current , as in a flashlight, or with time-varying currents. Important elements in circuits include sources of power called electromotive forces ; resistors , which control the flow of current for a given voltage; capacitors , which store charge and energy temporarily; and inductors, which also store electrical energy for a limited time. Circuits with these elements can be described entirely with algebra. (For more complicated circuit elements such as transistors , see semiconductor device and integrated circuit ). Two mathematical quantities associated with vector fields, like the electric field E and the magnetic field B, are useful for describing electromagnetic phenomena. They are the flux of such a field through a surface and the line integral of the field along a path. The flux of a field through a surface measures how much of the field penetrates through the surface; for every small section of the surface, the flux is proportional to the area of that section and depends also on the relative orientation of the section and the field.

The line integral of a field along a path measures the degree to which the field is aligned with the path; for every small section of path, it is proportional to the length of that section and is also dependent on the alignment of the field with that section of path. When the field is perpendicular to the path, there is no contribution to the line integral. The fluxes of E and B through a surface and the line integrals of these fields along a path play an important role in electromagnetic theory. As examples, the flux of the electric field E through a closed surface measures the amount of charge contained within the surface; the flux of the magnetic field B through a closed surface is always zero because there are no magnetic monopoles (magnetic charges consisting of a single pole) to act as sources of the magnetic field in the way that charge is a source of the electric field. Effects of varying magnetic fields The merger of electricity and magnetism from distinct phenomena into electromagnetism is tied to three closely related events. The first was Hans Christian Ørsted’s accidental discovery of the influence of an electric current on a magnetic needle—namely, that magnetic fields are produced by electric currents.

Ørsted’s 1820 report of his observation spurred an intense effort by scientists to prove that magnetic fields can induce currents. The second event was Faraday’s experimental proof that a changing magnetic field can induce a current in a circuit. The third was Maxwell’s prediction that a changing electric field has an associated magnetic field. The technological revolution attributed to the development of electric power and radio communications can be traced to these three landmarks. Faraday’s law of induction Faraday’s discovery in 1831 of the phenomenon of magnetic induction is one of the great milestones in the quest toward understanding and exploiting nature. Stated simply, Faraday found that (1) a changing magnetic field in a circuit induces an electromotive force in the circuit; and (2) the magnitude of the electromotive force equals the rate at which the flux of the magnetic field through the circuit changes. The flux is a measure of how much field penetrates through the circuit. The electromotive force is measured in volts and is represented by the equation Here, Φ, the flux of the vector field B through the circuit, measures how much of the field passes through the circuit.

To illustrate the meaning of flux, imagine how much water from a steady rain will pass through a circular ring of area A. When the ring is placed parallel to the path of the water drops, no water passes through the ring. The maximum rate at which drops of rain pass through the ring occurs when the surface is perpendicular to the motion of the drops. The rate of water drops crossing the surface is the flux of the vector field ρv through that surface, where ρ is the density of water drops and v represents the velocity of the water. Clearly, the angle between v and the surface is essential in determining the flux. To specify the orientation of the surface, a vector A is defined so that its magnitude is the surface area A in units of square metres and its direction is perpendicular to the surface. The rate at which raindrops pass through the surface is ρv cos θA, where θ is the angle between v and A. Using vector notation, the flux is ρv · A. For the magnetic field, the amount of flux through a small area represented by the vector dA is given by B · dA.

For a circuit consisting of a single turn of wire, adding the contributions from the entire surface that is surrounded by the wire gives the magnetic flux Φ of equation (1). The rate of change of this flux is the induced electromotive force. The units of magnetic flux are webers , with one weber equaling one tesla per square metre. Finally, the minus sign in equation (1) indicates the direction of the induced electromotive force and hence of any induced current. The magnetic flux through the circuit generated by the induced current is in whatever direction will keep the total flux in the circuit from changing. The minus sign in equation (1) is an example of Lenz’s law for magnetic systems. This law, deduced by the Russian-born physicist Heinrich Friedrich Emil Lenz, states that “what happens is that which opposes any change in the system.” Faraday’s law is valid regardless of the process that causes the magnetic flux to change. It may be that a magnet is moved closer to a circuit or that a circuit is moved closer to a magnet. Figure 4 shows a magnet brought near a conducting ring and gives the direction of the induced current and field, thus illustrating both Faraday’s and Lenz’s laws.

Another alternative is that the circuit may change in size in a fixed external magnetic field or, as in the case of alternating-current (AC) generation, that the circuit may be a coil of conducting wire rotating in a magnetic field so that the flux Φ varies sinusoidally in time. The magnetic flux Φ through a circuit has to be considered carefully in the application of Faraday’s law given in equation (1). For example, if a circuit consists of a coil with five closely spaced turns and if ϕ is the magnetic flux through a single turn, then the value of Φ for the five-turn circuit that must be used in Faraday’s law is Φ = 5ϕ. If the five turns are not the same size and closely spaced, the problem of determining Φ can be quite complex. Self-inductance and mutual inductance The self-inductance of a circuit is used to describe the reaction of the circuit to a changing current in the circuit, while the mutual inductance with respect to a second circuit describes the reaction to a changing current in the second circuit.

When a current i1 flows in circuit 1, i1 produces a magnetic field B1; the magnetic flux through circuit 1 due to current i1 is Φ11. Since B1 is proportional to i1, Φ11 is as well. The constant of proportionality is the self-inductance L1 of the circuit. It is defined by the equation The units of inductance are henrys . If a second circuit is present, some of the field B1 will pass through circuit 2 and there will be a magnetic flux Φ21 in circuit 2 due to the current i1. The mutual inductance M21 is given by The magnetic flux in circuit 1 due to a current in circuit 2 is given by Φ12 = M12i2. An important property of the mutual inductance is that M21 = M12. It is therefore sufficient to use the label M without subscripts for the mutual inductance of two circuits. The value of the mutual inductance of two circuits can range from +√L1L2 to −√L1L2, depending on the flux linkage between the circuits.

If the two circuits are very far apart or if the field of one circuit provides no magnetic flux through the other circuit, the mutual inductance is zero. The maximum possible value of the mutual inductance of two circuits is approached as the two circuits produce B fields with increasingly similar spatial configurations. If the rate of change with respect to time is taken for the terms on both sides of equation (2), the result is dΦ11/dt = L1di1/dt. According to Faraday’s law, dΦ11/dt is the negative of the induced electromotive force. The result is the equation frequently used for a single inductor in an AC circuit—i.e., The phenomenon of self-induction was first recognized by the American scientist Joseph Henry . He was able to generate large and spectacular electric arcs by interrupting the current in a large copper coil with many turns. While a steady current is flowing in a coil, the energy in the magnetic field is given by 1/2Li2. If both the inductance L and the current i are large, the amount of energy is also large.

If the current is interrupted, as, for example, by opening a knife-blade switch, the current and therefore the magnetic flux through the coil drop quickly. Equation (4) describes the resulting electromotive force induced in the coil, and a large potential difference is developed between the two poles of the switch. The energy stored in the magnetic field of the coil is dissipated as heat and radiation in an electric arc across the space between the terminals of the switch. Due to advances in superconducting wires for electromagnets , it is possible to use large magnets with magnetic fields of several teslas for temporarily storing electric energy as energy in the magnetic field. This is done to accommodate short-term fluctuations in the consumption of electric power. A transformer is an example of a device that uses circuits with maximum mutual induction. Figure 5 illustrates the configuration of a typical transformer. Here, coils of insulated conducting wire are wound around a ring of iron constructed of thin isolated laminations or sheets. The laminations minimize eddy currents in the iron. Eddy currents are circulatory currents induced in the metal by the changing magnetic field. These currents produce an undesirable by-product— heat in the iron.

Energy loss in a transformer can be reduced by using thinner laminations, very “soft” (low- carbon ) iron and wire with a larger cross section, or by winding the primary and secondary circuits with conductors that have very low resistance . Unfortunately, reducing the heat loss increases the cost of transformers. Transformers used to transmit and distribute power are commonly 98 to 99 percent efficient. While eddy currents are a problem in transformers, they are useful for heating objects in a vacuum . Eddy currents are induced in the object to be heated by surrounding a relatively nonconducting vacuum enclosure with a coil carrying a high-frequency alternating current. In a transformer, the iron ensures that nearly all the lines of B passing through one circuit also pass through the second circuit and that, in fact, essentially all the magnetic flux is confined to the iron. Each turn of the conducting coils has the same magnetic flux; thus, the total flux for each coil is proportional to the number of turns in the coil.

As a result, if a source of sinusoidally varying electromotive force is connected to one coil, the electromotive force in the second coil is given by Thus, depending on the ratio of N2 to N1 (where N1 and N2 are the number of turns in the first and second coils, respectively), the transformer can be either a step-up or a step-down device for alternating voltages. For many reasons, including safety, generation and consumption of electric power occur at relatively low voltages. Step-up transformers are used to obtain high voltages before electric power is transmitted, since for a given amount of power, the current in the transmission lines is much smaller. This minimizes energy lost by resistive heating of the conductors. Faraday’s law constitutes the basis for the power industry and for the transformation of mechanical energy into electric energy. In 1821, a decade before his discovery of magnetic induction, Faraday conducted experiments with electric wires rotating around compass needles. This earlier work, in which a wire carrying a current rotated around a magnetized needle and a magnetic needle was made to rotate around a wire carrying an electric current, provided the groundwork for the development of the electric motor .

Page 1 of 2 Dixline DemeShield EMI Coating | Dixline Corporation Dixline EMI-RFI Shielding Data with PVD process.pdf Vacuum Metallization Method of EMI shielding The main objective of any type of shielding is to prevent the passage of electromagnetic waves into or out of the device. EMI shielding can work by reflection, absorption, or by carrying the electromagnetic radiation to ground. The fundamental aim is to establish a Faraday cage (named after Michael Faraday who formulated the laws of electromagnetism) to provide an EMI shield. Metals were the original EMI shielding method and metal casings were, for many years, the only method of shielding electronic devices. Metal cans placed on the circuit board are still used in many cases to reduce EMI. However, their use must be considered early in the design stage and on some circuits the number of metal cans used can add significantly to the weight of the device. This can increase the difficulty of recycling the product during disposal. Plastics have made great inroads into the electronics enclosure market for a range of reasons such as: • Cost reduction. • Ease of production • Improved design freedom (integral and multiple colors, soft touch and product complexity).

Unfortunately, unlike metals, plastics are transparent to electromagnetic radiation and provide no inherent EMI shielding. The rapid rise in the use of plastics in portable consumer electronics has therefore driven the development of a variety of methods for EMI shielding of plastics. Dixline Corporation utilizes the advanced method of Vacuum metallization to establish a Faraday cage and EMI shielding. The specialized equipment of this application method applies a thin coating of aluminum to the surface of the plastic to provide a highly conductive layer and very effective EMI shielding. Aluminum is used because it has a very high conductivity and is highly corrosion resistant in most environments. Vacuum metallizing is a multiple stage process: 1. The part is cleaned, if required, to give good adhesion between the substrate and the vacuum deposited aluminum. 2. If selective coating is being used, the product is masked to cover any areas that do not require coating. 3. A layer of aluminum (up to 10 microns) is applied to the plastic surface to provide the conductivity and main EMI shielding. The process of vacuum metallizing Vacuum metallizing can be used for complex shapes, but often requires a mask to ensure that the metal is deposited in the correct locations.

This can be done either by custom mask tooling or by hand masking although custom mask tooling is preferred for larger volumes. Vacuum metallizing can also be carried out on thermoformed parts to form the equivalent of a metal can for board level EMI shielding. Applications EMI shielding is used for a wide variety of products such as: • Personal computer and mobile communication housings • Medical equipment housings

Question: Who formulated the laws of electromagnetism?
Answer: Faraday