ELECTRICITYMAGNETISMandELECTROMAGNETISM

Submitted by:Joel L. BalabaBS EcE 3-1Submitted to: Engr. Rose Ann Sumadsad

ELECTRICITYElectricityis the set ofphysicalphenomena associated with the presence and flow ofelectric charge. Electricity gives a wide variety of well-known effects, such aslightning,static electricity,electromagnetic inductionandelectrical current. In addition, electricity permits the creation and reception ofelectromagnetic radiationsuch asradio waves.In electricity, charges produceelectromagnetic fieldswhich act on other charges. Electricity occurs due to several types of physics: electric charge: a property of somesubatomic particles, which determines theirelectromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields. electric field(seeelectrostatics): an especially simple type of electromagnetic field produced by an electric charge even when it is not moving (i.e., there is noelectric current). The electric field produces a force on other charges in its vicinity. electric potential: the capacity of an electric field to doworkon anelectric charge, typically measured involts. electric current: a movement or flow of electrically charged particles, typically measured inamperes. electromagnets: Moving charges produce amagnetic field. Electrical currents generate magnetic fields, and changing magnetic fields generate electrical currents.Inelectrical engineering, electricity is used for: electric powerwhere electric current is used to energise equipment;

Electric charge The presence of charge gives rise to an electrostatic force: charges exert aforceon each other, an effect that was known, though not understood, in antiquity.[17]:457A lightweight ball suspended from a string can be charged by touching it with a glass rod that has itself been charged by rubbing with a cloth. If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart. Two balls that are charged with a rubbed amber rod also repel each other. However, if one ball is charged by the glass rod, and the other by an amber rod, the two balls are found to attract each other. These phenomena were investigated in the late eighteenth century byCharles-Augustin de Coulomb, who deduced that charge manifests itself in two opposing forms. This discovery led to the well-known axiom:like-charged objects repel and opposite-charged objects attract.[17] The force acts on the charged particles themselves, hence charge has a tendency to spread itself as evenly as possible over a conducting surface. The magnitude of the electromagnetic force, whether attractive or repulsive, is given byCoulomb's law, which relates the force to the product of the charges and has aninverse-squarerelation to the distance between them. The electromagnetic force is very strong, second only in strength to thestrong interaction,[25]but unlike that force it operates over all distances.]In comparison with the much weakergravitational force, the electromagnetic force pushing two electrons apart is 1042times that of thegravitationalattraction pulling them together. Study has shown that the origin of charge is from certain types ofsubatomic particleswhich have the property of electric charge. Electric charge gives rise to and interacts with theelectromagnetic force, one of the fourfundamental forcesof nature. The most familiar carriers of electrical charge are theelectronandproton. Experiment has shown charge to be aconserved quantity, that is, the net charge within anisolated systemwill always remain constant regardless of any changes taking place within that system.Within the system, charge may be transferred between bodies, either by direct contact, or by passing along a conducting material, such as a wire.The informal termstatic electricityrefers to the net presence (or 'imbalance') of charge on a body, usually caused when dissimilar materials are rubbed together, transferring charge from one to the other. The charge on electrons and protons is opposite in sign, hence an amount of charge may be expressed as being either negative or positive. By convention, the charge carried by electrons is deemed negative, and that by protons positive, a custom that originated with the work ofBenjamin Franklin.The amount of charge is usually given the symbolQand expressed incoulombs;each electron carries the same charge of approximately 1.60221019coulomb. The proton has a charge that is equal and opposite, and thus +1.60221019 coulomb. Charge is possessed not just bymatter, but also byantimatter, eachantiparticlebearing an equal and opposite charge to its corresponding particle. Charge can be measured by a number of means, an early instrument being thegold-leaf electroscope, which although still in use for classroom demonstrations, has been superseded by the electronicelectrometer

Electric field The concept of the electricfieldwas introduced byMichael Faraday. An electric field is created by a charged body in the space that surrounds it, and results in a force exerted on any other charges placed within the field. The electric field acts between two charges in a similar manner to the way that the gravitational field acts between twomasses, and like it, extends towards infinity and shows an inverse square relationship with distance.However, there is an important difference. Gravity always acts in attraction, drawing two masses together, while the electric field can result in either attraction or repulsion. Since large bodies such as planets generally carry no net charge, the electric field at a distance is usually zero. Thus gravity is the dominant force at distance in the universe, despite being much weaker. Field lines emanating from a positive charge above a plane conductor An electric field generally varies in space,[37]and its strength at any one point is defined as the force (per unit charge) that would be felt by a stationary, negligible charge if placed at that point.[17]:469470The conceptual charge, termed a 'test charge', must be vanishingly small to prevent its own electric field disturbing the main field and must also be stationary to prevent the effect ofmagnetic fields. As the electric field is defined in terms offorce, and force is avector, so it follows that an electric field is also a vector, having bothmagnitudeanddirection. Specifically, it is avector field.[17]:469470 The study of electric fields created by stationary charges is calledelectrostatics. The field may be visualised by a set of imaginary lines whose direction at any point is the same as that of the field. This concept was introduced by Faraday,[38]whose term 'lines of force' still sometimes sees use. The field lines are the paths that a point positive charge would seek to make as it was forced to move within the field; they are however an imaginary concept with no physical existence, and the field permeates all the intervening space between the lines.[38]Field lines emanating from stationary charges have several key properties: first, that they originate at positive charges and terminate at negative charges; second, that they must enter any good conductor at right angles, and third, that they may never cross nor close in on themselves.[17]:479 A hollow conducting body carries all its charge on its outer surface. The field is therefore zero at all places inside the body.[24]:88This is the operating principal of theFaraday cage, a conducting metal shell which isolates its interior from outside electrical effects. The principles of electrostatics are important when designing items ofhigh-voltageequipment. There is a finite limit to the electric field strength that may be withstood by any medium. Beyond this point,electrical breakdownoccurs and anelectric arccauses flashover between the charged parts. Air, for example, tends to arc across small gaps at electric field strengths which exceed 30kV per centimetre. Over larger gaps, its breakdown strength is weaker, perhaps 1kV per centimetre.[39]The most visible natural occurrence of this islightning, caused when charge becomes separated in the clouds by rising columns of air, and raises the electric field in the air to greater than it can withstand. The voltage of a large lightning cloud may be as high as 100MV and have discharge energies as great as 250kWh.[40] The field strength is greatly affected by nearby conducting objects, and it is particularly intense when it is forced to curve around sharply pointed objects. This principle is exploited in thelightning conductor, the sharp spike of which acts to encourage the lightning stroke to develop there, rather than to the building it serves to protect

Electric PotentialThe concept of electric potential is closely linked to that of the electric field. A small charge placed within an electric field experiences a force, and to have brought that charge to that point against the force requireswork. The electric potential at any point is defined as the energy required to bring a unit test charge from aninfinite distanceslowly to that point. It is usually measured involts, and one volt is the potential for which onejouleof work must be expended to bring a charge of onecoulombfrom infinity. This definition of potential, while formal, has little practical application, and a more useful concept is that ofelectric potential difference, and is the energy required to move a unit charge between two specified points. An electric field has the special property that it isconservative, which means that the path taken by the test charge is irrelevant: all paths between two specified points expend the same energy, and thus a unique value for potential difference may be stated.The volt is so strongly identified as the unit of choice for measurement and description of electric potential difference that the termvoltagesees greater everyday usage.For practical purposes, it is useful to define a common reference point to which potentials may be expressed and compared. While this could be at infinity, a much more useful reference is theEarthitself, which is assumed to be at the same potential everywhere. This reference point naturally takes the nameearthorground. Earth is assumed to be an infinite source of equal amounts of positive and negative charge, and is therefore electrically unchargedand unchargeable. Electric potential is ascalar quantity, that is, it has only magnitude and not direction. It may be viewed as analogous toheight: just as a released object will fall through a difference in heights caused by a gravitational field, so a charge will 'fall' across the voltage caused by an electric field.[43]As relief maps showcontour linesmarking points of equal height, a set of lines marking points of equal potential (known asequipotentials) may be drawn around an electrostatically charged object. The equipotentials cross all lines of force at right angles. They must also lie parallel to aconductor's surface, otherwise this would produce a force that will move the charge carriers to even the potential of the surface.The electric field was formally defined as the force exerted per unit charge, but the concept of potential allows for a more useful and equivalent definition: the electric field is the localgradientof the electric potential. Usually expressed in voltspermetre, the vector direction of the field is the line of greatest slope of potential, and where the equipotentials lie closest together. Electric circuitsMain article:Electric circuit

A basicelectric circuit. Thevoltage sourceVon the left drives acurrentIaround the circuit, deliveringelectrical energyinto theresistorR. From the resistor, the current returns to the source, completing the circuit.An electric circuit is an interconnection of electric components such that electric charge is made to flow along a closed path (a circuit), usually to perform some useful task.The components in an electric circuit can take many forms, which can include elements such asresistors,capacitors,switches,transformersandelectronics.Electronic circuitscontainactive components, usuallysemiconductors, and typically exhibitnon-linearbehaviour, requiring complex analysis. The simplest electric components are those that are termedpassiveandlinear: while they may temporarily store energy, they contain no sources of it, and exhibit linear responses to stimuli.[47]:1516Theresistoris perhaps the simplest of passive circuit elements: as its name suggests, itresiststhe current through it, dissipating its energy as heat. The resistance is a consequence of the motion of charge through a conductor: in metals, for example, resistance is primarily due to collisions between electrons and ions.Ohm's lawis a basic law ofcircuit theory, stating that the current passing through a resistance is directly proportional to the potential difference across it. The resistance of most materials is relatively constant over a range of temperatures and currents; materials under these conditions are known as 'ohmic'. Theohm, the unit of resistance, was named in honour ofGeorg Ohm, and is symbolised by the Greek letter . 1 is the resistance that will produce a potential difference of one volt in response to a current of one amp.[47]:3035Thecapacitoris a development of the Leyden jar and is a device that can store charge, and thereby storing electrical energy in the resulting field. It consists of two conducting plates separated by a thininsulatingdielectriclayer; in practice, thin metal foils are coiled together, increasing the surface area per unit volume and therefore thecapacitance. The unit of capacitance is thefarad, named afterMichael Faraday, and given the symbolF: one farad is the capacitance that develops a potential difference of one volt when it stores a charge of one coulomb. A capacitor connected to a voltage supply initially causes a current as it accumulates charge; this current will however decay in time as the capacitor fills, eventually falling to zero. A capacitor will therefore not permit asteady statecurrent, but instead blocks it.[47]:216220Theinductoris a conductor, usually a coil of wire, that stores energy in a magnetic field in response to the current through it. When the current changes, the magnetic field does too,inducinga voltage between the ends of the conductor. The induced voltage is proportional to thetime rate of changeof the current. The constant of proportionality is termed theinductance. The unit of inductance is thehenry, named afterJoseph Henry, a contemporary of Faraday. One henry is the inductance that will induce a potential difference of one volt if the current through it changes at a rate of one ampere per second. The inductor's behaviour is in some regards converse to that of the capacitor: it will freely allow an unchanging current, but opposes a rapidly changing one.[47]:226229Electric powerMain article:electric powerElectric power is the rate at whichelectric energyis transferred by anelectric circuit. TheSIunit ofpoweris thewatt, onejoulepersecond.Electric power, likemechanical power, is the rate of doingwork, measured inwatts, and represented by the letterP. The termwattageis used colloquially to mean "electric power in watts." The electric power inwattsproduced by an electric currentIconsisting of a charge ofQcoulombs everytseconds passing through anelectric potential(voltage) difference ofVis

whereQis electric charge incoulombstis time in secondsIis electric current inamperesVis electric potential or voltage involtsElectricity generationis often done withelectric generators, but can also be supplied by chemical sources such aselectric batteriesor by other means from a wide variety of sources of energy. Electric power is generally supplied to businesses and homes by theelectric power industry. Electricity is usually sold by thekilowatt hour(3.6 MJ) which is the product of power in kilowatts multiplied by running time in hours. Electric utilities measure power usingelectricity meters, which keep a running total of the electric energy delivered to a customer.

MAGNETISMMagnetism refers to physical phenomena arising from the force between magnets, objects that produce fields that attract or repel other objects.All materials experience magnetism, some more strongly than others. Permanent magnets, made from materials such as iron, experience the strongest effects, known as ferromagnetism. This is the only form of magnetism strong enough to be felt by people.Then there's paramagnetism, in which certain materials are attracted by a magnetic field, and diamagnetism, in which materials are repelled by a magnetic field. Other, more complex, forms include antiferromagnetism, in which the magnetic properties of atoms or molecules align next to each other; and spin glass behavior, which involve both ferromagnetic and antiferromagnetic interactions. Some materials are called non-magnetic, because their magnetic effects are so small. Magnetism can also vary depending on temperature and other factors.Diamagnetism[edit]Main article:DiamagnetismDiamagnetism appears in all materials, and is the tendency of a material to oppose an applied magnetic field, and therefore, to be repelled by a magnetic field. However, in a material with paramagnetic properties (that is, with a tendency to enhance an external magnetic field), the paramagnetic behavior dominates.[8]Thus, despite its universal occurrence, diamagnetic behavior is observed only in a purely diamagnetic material. In a diamagnetic material, there are no unpaired electrons, so the intrinsic electron magnetic moments cannot produce any bulk effect. In these cases, the magnetization arises from the electrons' orbital motions, which can be understoodclassicallyas follows:When a material is put in a magnetic field, the electrons circling the nucleus will experience, in addition to theirCoulombattraction to the nucleus, aLorentz forcefrom the magnetic field. Depending on which direction the electron is orbiting, this force may increase thecentripetal forceon the electrons, pulling them in towards the nucleus, or it may decrease the force, pulling them away from the nucleus. This effect systematically increases the orbital magnetic moments that were aligned opposite the field, and decreases the ones aligned parallel to the field (in accordance withLenz's law). This results in a small bulk magnetic moment, with an opposite direction to the applied field.Note that this description is meant only as anheuristic; a proper understanding requires aquantum-mechanicaldescription.Note that all materials undergo this orbital response. However, in paramagnetic and ferromagnetic substances, the diamagnetic effect is overwhelmed by the much stronger effects caused by the unpaired electrons.Paramagnetism[edit]Main article:ParamagnetismIn a paramagnetic material there areunpaired electrons, i.e.atomicormolecular orbitalswith exactly one electron in them. While paired electrons are required by thePauli exclusion principleto have their intrinsic ('spin') magnetic moments pointing in opposite directions, causing their magnetic fields to cancel out, an unpaired electron is free to align its magnetic moment in any direction. When an external magnetic field is applied, these magnetic moments will tend to align themselves in the same direction as the applied field, thus reinforcing it.Ferromagnetism[edit]

A permanent magnet holding up several coinsMain article:FerromagnetismA ferromagnet, like a paramagnetic substance, has unpaired electrons. However, inadditionto the electrons' intrinsic magnetic moment's tendency to be parallel to anapplied field, there is also in these materials a tendency for these magnetic moments to orient parallel toeach otherto maintain a lowered-energy state. Thus, even in the absence of an applied field, the magnetic moments of the electrons in the material spontaneously line up parallel to one another.Every ferromagnetic substance has its own individual temperature, called theCurie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy-lowering due to ferromagnetic order.Ferromagnetism only occurs in a few substances; the common ones areiron,nickel,cobalt, theiralloys, and some alloys ofrare earthmetals.Magnetic domains[edit]

Magnetic domains boundaries (white lines) in ferromagnetic material (black rectangle).Main article:Magnetic domainsThe magnetic moment of atoms in aferromagneticmaterial cause them to behave something like tiny permanent magnets. They stick together and align themselves into small regions of more or less uniform alignment calledmagnetic domainsorWeiss domains. Magnetic domains can be observed with amagnetic force microscopeto reveal magnetic domain boundaries that resemble white lines in the sketch. There are many scientific experiments that can physically show magnetic fields.

Effect of a magnet on the domains.When a domain contains too many molecules, it becomes unstable and divides into two domains aligned in opposite directions so that they stick together more stably as shown at the right.When exposed to a magnetic field, the domain boundaries move so that the domains aligned with the magnetic field grow and dominate the structure (dotted yellow area) as shown at the left. When the magnetizing field is removed, the domains may not return to an unmagnetized state. This results in the ferromagnetic material's being magnetized, forming a permanent magnet.When magnetized strongly enough that the prevailing domain overruns all others to result in only one single domain, the material ismagnetically saturated. When a magnetized ferromagnetic material is heated to theCurie pointtemperature, the molecules are agitated to the point that the magnetic domains lose the organization and the magnetic properties they cause cease. When the material is cooled, this domain alignment structure spontaneously returns, in a manner roughly analogous to how a liquid canfreezeinto a crystalline solid.Antiferromagnetism[edit]

Antiferromagnetic orderingMain article:AntiferromagnetismIn an antiferromagnet, unlike a ferromagnet, there is a tendency for the intrinsic magnetic moments of neighboring valence electrons to point inoppositedirections. When all atoms are arranged in a substance so that each neighbor is 'anti-aligned', the substance isantiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field is produced by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.In some materials, neighboring electrons want to point in opposite directions, but there is no geometrical arrangement in whicheachpair of neighbors is anti-aligned. This is called aspin glass, and is an example ofgeometrical frustration.Ferrimagnetism[edit]

Ferrimagnetic orderingMain article:FerrimagnetismLike ferromagnetism,ferrimagnetsretain their magnetization in the absence of a field. However, like antiferromagnets, neighboring pairs of electron spins like to point in opposite directions. These two properties are not contradictory, because in the optimal geometrical arrangement, there is more magnetic moment from the sublattice of electrons that point in one direction, than from the sublattice that points in the opposite direction.Mostferritesare ferrimagnetic. The first discovered magnetic substance,magnetite, is a ferrite and was originally believed to be a ferromagnet;Louis Neldisproved this, however, after discovering ferrimagnetism.Superparamagnetism[edit]Main article:SuperparamagnetismWhen a ferromagnet or ferrimagnet is sufficiently small, it acts like a single magnetic spin that is subject toBrownian motion. Its response to a magnetic field is qualitatively similar to the response of a paramagnet, but much larger.Electromagnet[edit]Anelectromagnetis a type ofmagnetwhose magnetism is produced by the flow of electriccurrent. The magnetic field disappears when the current ceases.

Electromagnets attracts paper clips when current is applied creating a magnetic field. The electromagnet loses them when current and magnetic field are removed.Other types of magnetism[edit] Molecular magnet Metamagnetism Molecule-based magnet Spin glassMagnetism, electricity, and special relativity[edit]Main article:Classical electromagnetism and special relativity

Magnetism from length-contraction.As a consequence of Einstein's theory of special relativity, electricity and magnetism are fundamentally interlinked. Both magnetism lacking electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects aslength contraction,time dilation, and the fact that themagnetic forceis velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity.[6][9]In particular, a phenomenon that appears purely electric or purely magnetic to one observer may be a mix of both to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism, analogous to how relativity "mixes" space and time intospacetime.All observations on electromagnetism apply to what might be considered to be primarily magnetism, e.g. perturbations in the magnetic field are necessarily accompanied by a nonzero electric field, and propagate at thespeed of light.Magnetic fields in a material[edit]See also:Magnetic field H and B inside and outside of magnetic materialsIn a vacuum,

where0is thevacuum permeability.In a material,

The quantity0Mis calledmagnetic polarization.If the fieldHis small, the response of the magnetizationMin adiamagnetorparamagnetis approximately linear:

the constant of proportionality being called the magnetic susceptibility. If so,

In a hard magnet such as a ferromagnet,Mis not proportional to the field and is generally nonzero even whenHis zero (seeRemanence).Magnetic force[edit]

Magnetic lines of force of a bar magnet shown by iron filings on paperMain article:Magnetic fieldThe phenomenon of magnetism is "mediated" by the magnetic field. An electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.Maxwell's equations, which simplify to theBiotSavart lawin the case of steady currents, describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electricallycharged particlesare inmotionfor example, from movement of electrons in anelectric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic"magnetic dipolesarising from quantum-mechanicalspin.The same situations that create magnetic fieldscharge moving in a current or in an atom, and intrinsic magnetic dipolesare also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.When a charged particle moves through amagnetic fieldB, it feels aLorentz forceFgiven by thecross product:[10]

whereis the electric charge of the particle, andvis thevelocityvectorof the particleBecause this is a cross product, the force isperpendicularto both the motion of the particle and the magnetic field. It follows that the magnetic force does noworkon the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down. The magnitude of the force is

whereis the angle betweenvandB.One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling theindex finger"V", themiddle finger"B", and thethumb"F" with your right hand. When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively.

Magnetic fieldsA magnetic field is a way of mathematically describing how magnetic materials and electric currents interact. Magnetic fields have both a direction and a magnitude, or strength. Magnets have a "north" pole and a "south" pole. Opposite poles attract each other and alike poles repel each other. These poles are referred to as a magnetic dipole. Magnetic dipoles and electric currents both give rise to magnetic fields.A magnet is what makes acompasspoint north the small magnetic pin in a compass is suspended so that it can spin freely inside its casing and respond to our planet's magnetism. A compass needle aligns itself and points toward the top ofEarth's magnetic field.

Magnetic forceMagnetic fields exert a force on particles in the field, called the Lorentz force. The motion of electrically charged particles gives rise to magnetism. The magnetic force acting on a single electric charge depends on the size of the charge, its speed, and the strengths of the electric and magnetic fields.Electricity and magnetismBoth electric and magnetic interactions are elements of a single phenomenon called electromagnetism. There are four fundamental forces: the strong force, the weak force,gravitationand the electromagnetic force. The field of electromagnetism deals with how electrically charged particles interact with each other and with magnetic fields.James Clerk Maxwell developed a unified theory of electromagnetism in 1873. There are four main electromagnetic interactions: The force of attraction or repulsion between electric charges is inversely proportional to the square of the distance between them. Magnetic poles comes in pairs that attract and repel each other much as electric charges do. An electric current in a wire produces a magnetic field whose direction depends on the direction of the current. A moving electric field produces a magnetic field, and vice versa.Maxwell developed a set of formulas, called Maxwell's equations, to describe these phenomena.

ELECTROMAGNETISMElectromagnetismis the study of theelectromagnetic forcewhich is a type of physical interaction that occurs betweenelectrically chargedparticles. The electromagnetic force usually manifests aselectromagnetic fields, such aselectric fields,magnetic fieldsandlight. The electromagnetic force is one of the fourfundamental interactionsinnature. The other three are thestrong interaction, theweak interaction, andgravitation.[1]The wordelectromagnetismis a compound form of twoGreekterms, ,lektron, "amber", and ,magnetic, from "magntis lthos" ( ), which means "magnesian stone", a type ofiron ore. Thescienceof electromagnetic phenomena is defined in terms of the electromagnetic force, sometimes called theLorentz force, which includes bothelectricityandmagnetismas elements of one phenomenon.The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result ofintermolecular forcesbetween individualmoleculesin matter.Electronsare bound by electromagnetic wave mechanics into orbitals aroundatomic nucleito formatoms, which are the building blocks of molecules. This governs the processes involved inchemistry, which arise from interactions between theelectronsof neighboring atoms, which are in turn determined by the interaction between electromagnetic force and the momentum of the electrons.There are numerousmathematical descriptions of the electromagnetic field. Inclassical electrodynamics, electric fields are described aselectric potentialandelectric currentinOhm's law,magnetic fieldsare associated withelectromagnetic inductionand magnetism, andMaxwell's equationsdescribe how electric and magnetic fields are generated and altered by each other and by charges and currents.The theoretical implications of electromagnetism, in particular the establishment of the speed of light based on properties of the "medium" of propagation (permeabilityandpermittivity), led to the development ofspecial relativitybyAlbert Einsteinin 1905.Although electromagnetism is considered one of the four fundamental forces, at high energy theweak forceand electromagnetism are unified. In the history of the universe, during thequark epoch, theelectroweak forcesplit into the electromagnetic and weak forces.

Electromagnetism: in a key development for modern physics, electricity and magnetism were `unified' into electromagnetism the connection develops from the fact that an electric current (the flow of electrons in a metal) produces a magnetic field Faraday shows that a changing electric field produces a magnetic field and, vice-versus, a changing magnetic field produces an electric current Maxwell completes the theory with a full mathematical description of the relationship between electric and magnetic fields = electromagnetism

Maxwell's new theory provides a new description of light, as electromagnetic waves electromagnetism represents a sharp change in the way Nature is described, i.e. the use of invisible fields and understanding that can only be communicated with mathematics

Although conceived of as distinct phenomena until the 19th century,electricityandmagnetismare now known to be components of the unified theory ofelectromagnetism.A connection between electricity and magnetism had long been suspected, and in 1820 the Danish physicist Hans Christian Orsted showed that an electric current flowing in a wire produces its own magnetic field. Andre-Marie Ampere of France immediately repeated Orsted's experiments and within weeks was able to express the magnetic forces between current-carrying conductors in a simple and elegant mathematical form. He also demonstrated that a current flowing in a loop of wire produces a magnetic dipole indistinguishable at a distance from that produced by a small permanent magnet; this led Ampere to suggest that magnetism is caused by currents circulating on a molecular scale, an idea remarkably near the modern understanding.Faraday, in the early 1800's, showed that a changing electric field produces a magnetic field, and that vice-versus, a changing magnetic field produces an electric current. An electromagnet is an iron core which enhances the magnetic field generated by a current flowing through a coil, was invented by William Sturgeon in England during the mid-1820s. It later became a vital component of both motors and generators.The unification of electric and magnetic phenomena in a complete mathematical theory was the achievement of the Scottish physicistMaxwell(1850's). In a set of four elegant equations, Maxwell formalized the relationship between electric and magnetic fields. In addition, he showed that a linear magnetic and electric field can be self-reinforcing and must move at a particular velocity, the speed of light. Thus, he concluded that light is energy carried in the form of opposite but supporting electric and magnetic fields in the shape of waves, i.e. self-propagating electromagnetic waves.

In doing this, Maxwell moved physics to a new realm of understanding. By using field theory as the core to electromagnetism, we have moved beyond a Newtonian worldview where objects change by direct contact and into a theory that uses invisible fields. This introduces a type of understanding which can only be described with a type of mathematics that cannot be directly translated into language. In other words, scientists where restricted in talking about electromagnetic phenomenon strictly through the use of a new type of language, one of pure math.

Magnetic field due to anelectric currentMagnetic fields can be set up not only by permanentmagnets, as shown in Chapter 7, but also by electriccurrents.Let a piece of wire be arranged to pass verticallythrough a horizontal sheet of cardboard on which isplaced some iron filings, as shown in Fig. 8.1(a). If a currentis now passed through the wire, then the iron filingswill forma definite circular field patternwith thewire atthe centre,when the cardboard is gently tapped.By placinga compass in different positions the lines of flux areseen to have a definite direction as shown in Fig. 8.1(b).If the current direction is reversed, the direction ofthe lines of flux is also reversed. The effect on both theiron filings and the compass needle disappears when(a) (b)Iron filingsSheet ofcardboardWire CurrentdirectionFigure 8.1the current is switched off. The magnetic field is thusproduced by the electric current. The magnetic flux