 Hello, in this video lecture we are going to discuss with the expression for incentric impedance. Myself, Dr. Rupali Shalke working as an associate professor in electronics department at Walton Institute of Technology, Sholapur. Learning outcomes at the end of this session students are able to derive the equation for incentric impedance and also discuss the equation in different media. As wave in the media is associated with the electric field and magnetic field, so we can derive the impedance at any point by considering which is known as an incentric impedance. This incentric impedance is nothing but a ratio of magnitude of the electric field and magnitude of the magnetic field for a transverse electromagnetic wave in an unbounded media, which is mathematically given as a eta which is equal to the ratio of magnitude of E electric field to the magnitude of the magnetic field. Now, let us consider a wave is travelling in a x direction. If the wave is travelling in a x direction, then its electric field and magnetic field component in a x direction will be equal to 0 that is e x bar plus h x bar will be equal to 0 and the variations of the signals with respect to y and z will also be equal to 0. The resultant E will be either in a y direction or z direction that is a addition of electric field in a y direction and z direction. Same way the magnetic field h bar will be equal to h y a y bar plus h z a z bar. Now let us derive the incentric impedance using the Maxwell's equation. Now this Maxwell's equation which is derived from the Faraday's law which is given by del cross e bar is equal to minus b dou b by dou t. As we know the relation between the b and h b bar is equal to mu h bar that is why we have substituted the value for b b bar as a u mu h bar. Expanding the del cross h x bar and expanding the h in a Cartesian coordinate system. Now as we are assumed in the previous slide the value of dou by dou x and dou by dou z is equal to 0 and e x as a wave is propagating in x direction it will also be equal to 0. In a e x will also be 0 and h x on the RHS side it will also be equal to 0. Solving this equation we reduce to the equation y. Now we will compare here the a y a y terms and a z a z terms on LHS and RHS side. After comparison the a x term and a y term we get the equation 2 as dou e z by dou x is equal to mu dou h y by dou t which is a a x bar direction and in a a y direction it is a dou e y by dou x is equal to minus mu dou h z by dou t. Now let us assume the electromagnetic wave is travelling in a e y direction that is the electric field in a y direction. We will consider that electric wave as a e 0 e raise to minus gamma x where e this term is a amplitude of the signal as the wave is a sinusoidally represented which has a propagation that is why it is a minus gamma in a x direction. Now we will differentiate this equation 4 with respect to x then the differentiation will be dou e y by dou x is equal to minus gamma e y. Now we will see that here it is dou e y by dou x and same here dou e y by dou x that is why we will compare equation 3 and equation 5. After comparison it will be minus gamma e y will be equal to minus mu dou h z by dou t. The minus signs will cancel out and only we will remain and here we substitute dou by dou t is equal to j omega. Now we will take the ratio of e y by h z that is e by h which is nothing but the eccentric impedance. The eccentric impedance is equal to e y by h z as it is in a y direction this is in a z direction the equation we will be getting is a intensive impedance will be j omega mu upon gamma. Now as e is measured in volts per meter and magnetic field is measured in a ampere per meter the unit for the eccentric impedance will be volts per ampere that is ohms and it is called as a eccentric impedance of the media. Now the media can be the free space or media can be the conducting. Now let us see what will be the values of the eccentric impedance if the medias are being different. Now let us consider for the conducting media for the conducting media the propagation constant that is gamma is given by under root j omega mu sigma plus j omega epsilon where sigma is nothing but a conductivity substituting the value in the above equation of the gamma in above equation here we will substitute as a gamma value to equate and to cancel out the terms we will expand this in terms of root so that these two terms will be same which will be cancel out and only we will remain with the these two terms which is under root j omega mu upon sigma plus j omega epsilon this is a eccentric impedance for the conducting media. Now let us consider for the free space for the free space our assumption is sigma conductivity is equal to 0 and mu is equal to mu 0 and epsilon is equal to epsilon 0. In this equation we will substitute the values then it will be 0 and only you remain by mu by epsilon mu by epsilon mu 0 by epsilon these two terms are same that is why they will cancel mu 0 is nothing but a constant values and epsilon is also having the constant value which is given by mu 0 is equal to 4 pi into 10 raise to minus 7 and epsilon is equal to 8.84 into 10 raise to minus 12 by solving this we get it 120 pi or which is also equal to 377 ohms that is the eccentric impedance for free space is nothing but a 377 ohms from this we conclude that when eta is greater than 1 this indicates that the electric field is always greater than the magnetic field if in free space it is always a 377 times greater than the magnetic field that is why E is always dominating over the H therefore the electromagnetic wave equations are always expressed in terms of E that is electric field. Now if eta is the real value then E and H are in phase. Now pause this video let us consider the proof that for electromagnetic waves E dot H bar is equal to 0 and E cross H bar is having some direction of the propagation of the wave think over this as in the previous slides we are consider electric field magnetic field the relation between these two components is E y by H z is equal to eta here we are consider electric field in a y direction magnetic field in a z direction it will be eta will be E y by H z thus rewriting this terms E y will be equal to eta H z similarly now we will assume that electric field in a z direction and magnetic field in a y direction it will be minus eta phase change that is why it will minus eta same way we rewrite that equation. Now what is E dot H dot H dot will be equal to E y H y in a y direction and E z H z in a z direction the combination of the addition of that two from this equation we will substitute E y as a eta H z and from this equation we will substitute E z as a minus eta H y which will reduce to this equation this will be similar term that is why they get cancel out and the resultant is 0 same way let us expand del cross H bar as E x is we are assume the wave equation in x direction E x will be equal to 0 and H x will also be equal to 0 solving this we get E y H z minus H z H y in a x direction similarly we will substitute the values of E y in this equation this minus and this minus it get added then we will get eta common H square into A x if you see that the eccentric impedance and magnetic field are used in the direction of the x direction as the wave is propagating in a x direction that is why we say that the vector is E cross H bar is having the direction in x direction with the magnitude equal to n time the square of the magnetic field intensity which we have been asked to prove these are the references thank you.