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8. Electromagnetie Waves, Introduction -, Oersted experimentally predicted that the, electric current produces a magnetic field. Faraday from, his experiment 'on electromagletic induction fomd that, a changing maagnetic field produces an electric field., At, this time the clerk Maxwell state that the, magnetic field is not only produced by electric current, buł also by a fime electric field., varying, Maxwell formulated a set of eguations involuing, electric and magnetic fields and their sources (the Charge, and current). These, equations. These equations along with Lorentz force, formula , explain mathematicall& all the basic laws of, biectromagnetism., èquations are Known as Maxwell's, Maxwell through his equations come out with, a most impor tant prediktion ie. the existence of electro-, magnetic waves, which, clase to the speed oflight (3x10° mis). By this the, Can propagate in space with a speed, very, Mažwell conclude that light, is a electromagnetic wave., Maxwell's Equations and Lorentz Force -, (1), This equation is Gauss's Law in electrostatics. This gives, the volue' of total, electric flux in terms of the charge, enclosed by the surface s., (2 ), This equation is Gauss's Law in magnetostatics., This law shaw that the number of magnětic fieldlines, entering a closed surface is equal to number of magnetic, field lines leaving it: It confirms the absence of mågnetic, monopole., Scanned with CamScanner
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(3), $ E., This equation is, induction., Faraday's Law of electro magnetic, This law gives a relation between electric field and, a changing magnetic flux. It shows that the line, integral of electric field around any closed path (ie. emf), is bqualto the time rate of change f magnetic flux, through the Surface bounded by the' clošed Bath., (4 ), z Ho I + lo ID, Is = Eo[, This equation is generalised form of Ampere's, circuital Law, modi fied by Maxwell and is Known as, Ampere'- Maxwell law., This law shows that the line integral of +the, magnetic field around any closed path is related to, the conduction current (I) and displacement current (Is), through the path., (5), Lorentz Formula, Scanned with CamScanner
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Electromagnetic Waves -, According to maxwell, the electromagnetic, are those waves in which there are sinusoidal, waves, variation of electric and magnetic field vectors at right, angles to ěach other as wello as af rignt angles to the, difection of wave propagation., Direction of., Propogation, Both these fields LĒ and B) vary with time and, space and have the same, frequency., The electromagnetic waves, can propagati through the, space with the Ospeed of light '(3xi08s., Maxwell also found that the electromagnetic waves, should travel in free space (or vacuum) with a speed, given by, dot light (3xio, where Mo and Eo are permeability and permittivity, of the free space respectively., Mo =, 4r x107 Wb/Am, Eo = 8.85 X1D, 12 2/Nm, The velocity of EM waves in medium =, ME, where u and e are the absolute permeability omd, permittivity of the medium., Scanned with CamScanner
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Production of Electromagmetic wavas -, An electric charge at rest has electric field, in the region around it but no magnetic field. A, moving change produces both the electic and, fields., magnetic, If a change is moving with a Constant veločity, ( Current is not changing with time), the electric and, magnetic fields willUn8t change with time, hence no, electromagnetic waves, can be produced., But if the charge is moving with a non-zero, acceleration , both the magnetic field and electic fied, will with space and time, it then produces, change, electromagnetic waves., electromagnetic waves., Hence, an accelerated emits, charge, The, L-C circuit is an oscillatory circuit where, the charge is oscillating across the capacitor plates., An oscillating charge, in, acceleration hence Cit emitts electromagnetic waves,, which have the same, ascillating charge., L-C circuit has a non-zero, frequency, as that of the, frouombauf, , an electron cohile orbiting around, a stable orbit, does not emit electro, waves. Electromagnetic waves are emitled only, when it falls from higher energy orbit to lower, In an atom, the nucleus in, magnetic, energy, orbit., Electromagnetic waves are also produced when, fast moving elěctrons are suddenly stopped on the, metal tanget of higher atomic number., Scanned with CamScanner
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Properties of Electromagne tic Waves -, (1) The electromagnetic waves are produced by the, accelerated, or oscillating charge., (2) The EM wares do not require any material, medium for propagation., (3) These waves, speed, by the reloation -, travel in free space with a, 3x 108 m/s (speed of lignt) and is given, C, (4), In elechomagnetic wares the simu soidal variation, in both electric and magnetic tield vectors (E B), occurs, simultaneously. AS, the maximum and minimum values at the same place, and at the same time., a result they attains, a, The amplituodes ok the electric and magnetic fiekds, in free space are related by, C =, The equation of elect ric field and magnetic field, varrying simusoidally with x and t căn be given, as -, By, B. Sin (wt+Kx), K = 2*, and, E. Sin (wt+ K), Ez, The direction of variatiom of electric and magnetic, field vectors are perpendicular to each other, well as perpendicular' to the direction of propagation, ok waves. Therefore , electromagnetic waves are trans-, verse in nature' like light waves., as, (6) The electromagnetic wares carry energy, cohich is, divided egually° between electric field and magnetic, field vectors., Scanned with CamScanner
