ECUATIILE LUI MAXWELL PDF

Picturing the electric field by its field lines, this means the field lines begin at positive electric charges and end at negative electric charges. In terms of field lines, this equation states that magnetic field lines neither begin nor end but make loops or extend to infinity and back. In other words, any magnetic field line that enters a given volume must somewhere exit that volume. Equivalent technical statements are that the sum total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

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Picturing the electric field by its field lines, this means the field lines begin at positive electric charges and end at negative electric charges. In terms of field lines, this equation states that magnetic field lines neither begin nor end but make loops or extend to infinity and back. In other words, any magnetic field line that enters a given volume must somewhere exit that volume. Equivalent technical statements are that the sum total magnetic flux through any Gaussian surface is zero, or that the magnetic field is a solenoidal vector field.

Not to scale. The dynamically induced electric field has closed field lines similar to a magnetic field, unless superposed by a static charge induced electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators : for example, a rotating bar magnet creates a changing magnetic field, which in turn generates an electric field in a nearby wire. Each core stores one bit of data.

In integral form, the magnetic field induced around any closed loop is proportional to the electric current plus displacement current proportional to the rate of change of electric flux through the enclosed surface. The speed calculated for electromagnetic waves, which could be predicted from experiments on charges and currents, [note 3] matches the speed of light ; indeed, light is one form of electromagnetic radiation as are X-rays , radio waves , and others.

Maxwell understood the connection between electromagnetic waves and light in , thereby unifying the theories of electromagnetism and optics. Formulation in terms of electric and magnetic fields microscopic or in vacuum version [ edit ] In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of nature , the Lorentz force law, describes how, conversely, the electric and magnetic fields act on charged particles and currents.

A version of this law was included in the original equations by Maxwell but, by convention, is included no longer. The vector calculus formalism below, the work of Oliver Heaviside , [4] [5] has become standard. The relativistic formulations are even more symmetric and manifestly Lorentz invariant. For the same equations expressed using tensor calculus or differential forms, see alternative formulations.

The differential and integral formulations are mathematically equivalent and are both useful. The integral formulation relates fields within a region of space to fields on the boundary and can often be used to simplify and directly calculate fields from symmetric distributions of charges and currents.

On the other hand, the differential equations are purely local and are a more natural starting point for calculating the fields in more complicated less symmetric situations, for example using finite element analysis.

The equations introduce the electric field , E, a vector field , and the magnetic field , B, a pseudovector field, each generally having a time and location dependence. The universal constants appearing in the equations the first two ones explicitly only in the SI units formulation are:.

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Ecuatiile lui Maxwell

Evolutia potentialului este in intarziere in raport cu cea a surselor cu un interval de timp egal cu durata de propagare a semnalului de la surse pana la punctul M. Semnalul se propaga cu viteza egala cu viteza de propagare a luminii in vid. Fenomenul de propagare este una din consecintele importante a ecuatiilor lui Maxwell. Daca evolutia in timp a surselor este suficient de lenta, adica durata de propagare este foarte mica fata de o durata T caracteristica pentru aceasta evolutie, se poate admite ca potentialul si deci si campul urmaresc instantaneu evolutia surselor. Aceasta aproximatie este numita aproximatia regimului quasistationar. Electrodinamica in regim cuasistationar In aproximatia cuasistationara, indicatia data de un ampermetru plasat in serie in circuit este independenta de pozitia aparatului de masura. Daca circuitul are o intrerupere provocata de un condensator, intensitatea masurata este egala si cu fluxul termenului de deplasare in spatiul vid dintre armaturi.

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ECUATIILE LUI MAXWELL

Raporteaza o eroare J. C Maxwell dupa ce a studiat cercetariile in electricitate ale lui Faraday a pornit sa formuleze matematic o noua teorie a electricitatii si a magnetismului. El nu s-a putut folosi in demonstratiile sale de relativitate deoarece aceasta nu fusese inca descoperita,structura materiei era un mister iar relatia dintre lumina si electromagnetism nu era inca cunoscuta. In timp ce teoria lui Maxwell s-a d[ Maxwell era interesta de campul magnetic in substanta solida ca si in vid sic and vorbeste despre un curent de deplasare el include adesea de asemenea o oarecare sarcina in miscare. Ecuatiile matematice ale lui Maxwell au fost perfect clare si neabigue si introducerea curentului de deplasare a fost o descoperire teoretica importanta. Descrierea campului electromagnetic realizat de Maxwell a fost in mod essential complet.

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Proiectarea unei fundatii izolate Ecuatiile lui Maxwell Prin camp electromagnetic se intelege o forma de existenta a materiei domeniul respectiv fiind caracterizat prin 4 vectori: Se admite ca acesti vectori sunt continui in functie de loc si timp in orice punct al spatiului si ca derivatele lor sunt continue. Campul electromagnetic , ca sistem format din campul electric si cel magnetic, este un sistem fizic diferit de corpuri care poate exista in interiorul corpurilor cat si in vid. Acest camp poate fi generat de corpuri care se gasesc in anumite stari sau poate avea o existenta independenta. Marimile se vor considera vectori de camp fundamentali iar marimile se pot obtine din acestia , impreuna cu proprietatile mediului in care exista campul.

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Ecuațiile lui Maxwell

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