DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING

Transcription

1 DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING EE 630 ELECTROMAGNETIC THEORY UNIT-I ELECTROSTATICS I PART A. Mention an two souces of electomagnetic fields (o) What ae the souces of vaious tpes of EMF? Cuent caing conductos. Mobile phones. Micowave oven. Compute and Television sceen. High voltage Powe lines.. How can a vecto field be epessed as the gadient of a scala field? The gadient of an scala function is the maimum space ate of change of that function. If the scala V epesents electic potential, V epesents potential gadient. This opeation is called the gadient. Gadient of a scala is a vecto. 3. What is the phsical significance of the tem divegence of a vecto field? The divegence of the vecto field is the outflow fom a small closed suface pe unit volume as the volume shinks to zeo. 4. Define cul of a vecto. The cul of a vecto A at an point is defined as the limit of its suface integal of its coss poduct with nomal ove a closed suface pe unit volume as the volume shinks to zeo. A Cul A 5. Show that the vectos A and B ae paallel A = a + 4a + a z ; B = 4a + 8a +a z. Theefoe vectos A and B ae paallel to each othe. 6. Pove that cul gad Ф = 0 a a z a A B 4 = [8-8] [4-4] + [6-6] = 0 a 4 z a 8 a z a a a z z

2 Thus poved = ( ) a z z = 0 ( ) a z z ( ) az 7. How the unit vectos ae defined in clindical Co-odinate sstems? Unit vectos is having unit magnitude and diected along the co-odinates aes. Fo clindical Co-odinate Whee 8. Given A (Ma/June 009) a A a A a Z Az a, a & a z, ae unit vectos in the diection of,, z espectivel. A 0a 3a z and B5a 4a find the angle (o) pojection of A and B The angle Ө AB can be found b eithe dot o coss poduct A. B = (0, 0, 3). (5, 4, 0) = 40 A B 4 4 COS Ө AB = A. B A. B = Ө AB = Calculate the total chage within the volume of the univese, if v e 3 c m Fo Sphee dv = sinө d dө dф Total chage Q = v Vol e 0 dv = d sin d d 0 0

3 Q =.73π coulomb 0. What ae the tpes of co-odinate sstems? Catesian (o) ectangula co- odinate sstem Clindical co- odinate sstem Spheical co- odinate sstem. What is the diffeence between scala and vecto quantit? S.No. Scala Vecto. It is a quantit which is completel chaacteized b its magnitude. It is a quantit which is completel chaacteized b its magnitude and diection.. Eample: mass, volume, densit. Eample: foce, velocit, displacement.. Given the two coplana vecto A=3a +4a -5a z ; B=-6a +a +4a z ; Obtain the unit vecto nomal to the plane of the vectos A and B. AB = B A = (6-3)a + (-4)a + (4+5)a z AB = -9a -a +9a z AB =.88 Unit vecto = AB AB = a a a z 3. Convet the given point A(,, 3 ) in spheical co-odinates into Catesian co-odinates Given = Tansfom = sinө cosф = sin ( ) cos ( 3 ) Ө = = = sinө sinф = sin ( ) sin ( 3 ) Ф = 3 =.00 z = cosө = cos ( ) =.99

4 Catesian co-odinates ae (0.055,.00,.99). 4. State divegence theoem. The integal of the nomal component of an vecto field ove a closed suface is equal to the integal of the divegence of this vecto field ove a volume enclosed b the closed suface. 5. State stoke s theoem. The line integal of a vecto aound a closed path is equal to the suface integal of the nomal component of its cul ove an suface bounded b the path. 6. Epess the value of diffeential length, suface in ectangula co-odinate sstem. d d dz The diffeential length dl = The diffeential aea ds = d d = d dz = dz d 7. Epess the Gadient of a vecto in the thee sstem of othogonal co-odination. Fo Catesian coodinates sstem Fo clindical coodinates sstem Fo spheical coodinates sstem 8. Show that the two vectos A 6a a 5a and B 3( a a a ) each othe. z z ae pependicula to A. B = (6 3) + ( (-3)) + ((-5) ) = 0

5 9. Find the gadient of the scala field, A = Z COS A A A. A a a az z = ( z cos ) a ( z cos ) a ( z cos ) az z 0. Define vecto field. A = z[sin cos ] cos If a quantit which is specified in a egion to design a field is a vecto, then the coesponding field is called vecto field. E: The velocit of paticles in a moving fluid, wind velocit of atmosphee, displacement of a fling bid in a space.. State Gauss s Law The electic flu passing though an closed suface is equal to the total chage enclosed b that suface Q PART B. What ae the diffeent co-odinate sstems used to epesent field vectos? Discuss about them in bief.. Find the gadient of the following scala fields: (i) V = e -z sin cosh (ii) U = Z COS (iii) W = 0 sin θ cosф 3. Detemine the divegence of these vecto fields: (i) P = z a + z a z (ii) Q = sin a za z a cos z (iii) T = cos a sin cos a cos a 4. State and Eplain Divegence and Stoke s theoems 5. Given A cos I I in clindical co-odinate. Fo the contou shown veif Stoke s theoem. 6. Given points P(-,6,3) and vecto A=a +(+z)a, epess P and A in clindical and spheical coodinates. Evaluate A at P in the Catesian, clindical and spheical sstems.

6 7. Check validit of the divegence theoem consideing the field D= a+ a c/m and the ectangula paallelepiped fomed b the planes =0,=,=0,= &z=0,z=3 8. Veif the divegence theoem fo the following case A=XY a +Y 3 a +Y Za z and the suface is a cuboid defined b 0<<, 0<< & 0<z< 9. Given that F= X Ya -Ya. find F. dl whee L is shown in fig. & also veif the stoke s theoem. 0.Dive an epession fo the electic field due to a staight and infinite Unifoml chaged wie of length L metes and with a chage densit of +λ c/m at a point P which lies along the pependicula bisecto of wie.. Using Gauss s law calculate the E due to infinitel lage unifoml chaged plate.. Find the Electic potential at a point (4,3)m due to a chage of 0-9 clo at the oigin in fee space. 3. Thee point chages Q =0-6 c,q =-0-6 c and Q 3 = c ae located in ai (fee space) at the cones of an equilateal tiangle of 50cm side. Detemine the magnitude and diection of the foce on Q 3, Also find Electic field at Q ( i) A cicula disc of adius a, m is chaged unifoml with a chage densit of σ C/m Find the electic field intensit at a point h, m fom the disc along its ais. (ii) A cicula disc of 0 cm adius is chaged unifoml with a total chage of 0-6 c. Find the electic intensit at a point 30 cm awa fom the disc along the ais.

7 EE 630 ELECTROMAGNETIC THEORY UNIT-II ELECTROSTATICS II PART A. Define Electic field intensit o Electic field. The electic field intensit o the electic field stength at a point is defined as the foce pe unit chage. That is. What is the pactical significance of dielectic stength? The minimum value of the applied electic field at which the dielectic beakdown occus is Called dielectic stength. 3. What is an Electic dipole? Dipole o Electic dipole is nothing but two equal and opposite point chages ae sepaated b a ve small distance. 4. Define polaization Polaization is defined as dipole moment pe unit volume 5. State Coulomb s Law The foce between two pat chages is popotional to the poduct of chages and is invesel popotional to the squae of distance between them. 6. Wite down the epessions fo Laplace s and Poisson s equations Poisson s equations : Laplace s equations

8 7. State the vecto fom of electic flu densit The electic flu densit is defined as electic flu pe unit aea. It is denoted b D D=Q/A (c/m) the flu densit vecto is defined as: 8. Wite the capacitance in a coaial cable? C 0 ln( b / a) F/m 9. A unifom line chage with P L = 5 c / m lies along the -ais. Find E at (3,,)m. Given data: P L = 5 c / m Find: Fomula: E (Electic field intensit) =? E l 0 = (3,,)m E = (V/m) What is the significance phsical diffeence between Poisson s and Laplace s equation? Poisson s and Laplace equation ae useful fo detemining the electostatic potential V in egions at whose boundaies ae known. When the egion of inteest contains chages in a known distibution v can be used to detemine the potential function. Poisson s equation. The electical potential nea the oigin of a sstem of co-odinates is V=a +b +cz.find the field at (,4,6). Given data: V=a +b +cz (,,z) = (,4,6) Find : Field (E) =? Fomula: E = V E = V = V a V a V a z V = ( a a b a cz a ) At (,4,6) E = (a a 4b a 6c a ) V/m. z z z a a b a cz az

9 . Wite the poisson s & laplace's equations. Poisson s equation: Whee V - V V is the potential is the volume chage densit v is the dielectic constant o pemittivit of the medium. Laplace's equations: V 0 3. Wite down the magnetic bounda conditions. i) The nomal components of flu densit B ae continuous acoss the bounda. ii) The tangential components of field intensit H is continuous acoss the bounda 4. Define potential Potential at an point is defined as the wokdone is moving a unit positive chage fom infinit to that point in an electic field. Q V 4 5. Define capacitance It is defined as the atio of magnitude of chage on eithe of the conducto to the potential diffeence between conductos. It is given b Q C V 6. Descibe what ae the souces of electic field and magnetic fields. Stationa chages poduce electic field that ae constant in time: hence the tem electostatics. Moving chages (stead cuents) poduce magnetic fields that ae constant in time; hence the tem magnetostatics.

10 7. If V [ 0 Given data: find E and D V 0 Find : E & D =? Fomula: E = V D E V V V V = a a az z E = - 0 [ ( ) ( ) ( ) ] z = 40 ] ) ) ( ( D = 40 [ ] ) ) ( ( 8. Name a few applications of Gauss s Law in electostatics. Gauss s Law is applied to detemine the electic field intensit fom a closed suface.(e.g) Electic field can be detemine fo shell, two concentic shell o clindes, etc. 0. What is the use of Gauss s Law? Gauss s law is paticulal useful in detemining the electic field E of a chage distibution with some smmet condition. PART B ) (a) A total chage of 0-8 C is distibuted unifoml along a ing of adius of 5m. Calculated the potential on the ais of the ing at a point 5m fom the cente of the ing. (b) Conducting spheical shells with adii a=0cm and b=30cm ae maintained at a potential diffeence of 00V such that V (=b) = 0 and V (=b) = 00 volts. Detemine V and E in the egion between the shells. ) (a) Point chages mc and -mc ae located at (3,,-) and (-,-,-4) espectivel. Calculate the electic foce on a 0Nc chage located at (0,3,) and the electic field intensit at that point. (b) A dielectic sphee ( 5. 7 ) of adius 0cm has a point chage PC placed at its cente. Calculate: (i) The suface densit of polaization chage on the suface of the sphee (ii) The foce eeted b the chage on a -4 Pc point chage placed on the sphee.

11 3) (a) Deive the bounda conditions at the chage inteface of two dielectic media. (b) State and pove Gauss s Law 4) Discuss Electic field in fee space, dielectic and in conductos. 5) Conducting spheical shells with adii a=0cm and b=30cm ae maintained at a potential diffeence of 00v such that V(=b)=0 and V(=a)=00volts. Detemine v and E in the ejoin between the shells. 6) Detemine the capacitance of a capacito consisting of two paallel metal plates 30cm 30cm suface aea sepaated b 5mm in ai. What is the total eneg stoed b the capacito if the capacito is chaged to a potential diffeence of 500v? 7) What is dipole moment? Obtain epession fo the potential and field due to an electic dipole.two point chages Q = 4nC, Q = nc ae kept at (, 0, 0) and (6, 0, 0). Epess the electic field at (4, -, ) 8. Deive epession fo potential due to a dipole. 9. Deive epession fo eneg and eneg densit in a electic field. 0. Deive an epession fo capacitance between two paallel wies.. Deive the electic bounda conditions.

12 EE 630 ELECTROMAGNETIC THEORY UNIT-III MAGNETOSTATICS PART A. State Biot Savat law. It states that the magnetic flu densit at an point due to cuent element is popotional to the cuent element and sine of the angle between the element length and line joining and invesel popotional to the squae of the distance between them. I dl 0 db sin 4. State Ampee s cicuital law Magnetic field intensit aound a closed path is equal to the cuent enclosed b the path. H.dl I 3. Define the tem Magnetization. Magnetisation is defined as the atio of magnetic dipole moment to unit volume. A M Q a ( ) M Volume m A 4. What do ou mean b magnetic moment? A small ba magnet of length l with pole stength Qm ma be consideed as magnetic dipole. The poduct of pole stength Qm and length l is called magnetic moment. m = Q m l Magnetic dipole is consideed as equivalent to cuent loop with aea A and caing a cuent I. The magnetic moment is, m = I A 5. Give fou similaities between Electostatic field magnetic field. Sl.No. Electo Static field Magnetic field Eneg stoed is ½ CV Eneg stoed is ½ LI Chages ae at est Chages ae at motion 3 Electic flu densit E V/m Magnetic flu densit H A/m 4 Electic flu densit D = E C/m Magnetic flu densit B = H Wb/m 6. What is H due to a long staight cuent caing conducto. The Magnetic field intensit at an point due to long staight conducto of caing cuent of I with a distance of d is I H d 7. Distinguish between magnetic scala potential and magnetic vecto potential. Sl.No. Magnetic scala potential Magnetic vecto potential It is defined as dead quantit whose negative gadient gives the magnetic intensit if thee is no cuent souce pesent. It is defined as that quantit whose cul gives the magnetic flu densit H BA Vm m

13 8. State Loent s Law and application If a chage paticle is moving with velocit v in the pesence of both an electic field E and a magnetic field B, then the total electomagnetic foce acting on it is F Q( E v B) This is called Loentz foce. Applications: i. Used to detemine electon o bits in magneton. ii. Used to detemine poton path in ccloton. iii. iv. Used to detemining plasma chaacteistics in a magneto hdodnamic geneato. Used to detemine the motion of chaged paticle in a combined electic and magnetic field. 9. A long staight wie caies a cuent I= Amp. At what distance is the magnetic field H= A/m. Given data: I = Amp H= A/m. Find : d =? Fomula: I I H = d = d H d = = 0.59 Result: d = 0.59 m 0. Detemine the foce pe unit length between two long paallel wies sepaated b 5cm in ai and caing cuents of 40A in the same diection. Given data: Find : Fomula: Result: I = I = 40 A d= A/m. Foce/length =? Foce/length = I 0 I d Foce/length = - 5 Foce/length = N/m = Define self inductance. The self inductance of a coil is defined as the ate of total magnetic flu linkage to the cicuit though the coil. L N i Whee, --- Magnetic flu N --- No. of tuns of coil I --- Cuent

14 . Define mutual inductance. The mutual inductance between two coils is defined as the ate of induced magnetic flu linkage in one coil to the though in othe coil. M N i Whee, N ---- No.of tuns in coil magnetic flu links coil i ---- cuent though coil 3. Compae the eneg stoed in inducto and capacito. Fo magnetic field, Eneg stoed in inducto W = ½ LI Fo electic field, Eneg stoed in capacito W = ½ CV 4. A egion in fee space has a magnetic field intensit of B web/m. What is the eneg stoed pe m 3 of space? Eneg densit = eneg pe volume = ½ B Joules/m 3 Whee, ---- is the pemeabilit of the medium. B ---- magnetic field intensit 5. Calculated the emf induced in a cicuit in a cicuit having an inductance of 700 H cuent though it vaies at a ate of 5000 A pe second. Given data: L = 700 H if the Find : Fomula: Result: di 5000 A/ s dt Induced emf ( v ) =? v L di dt v = v = 3.5 volts. 6. What will be the magnetic field of a tooidal solenoid ( with N tuns, caing a cuent I) within the volume of the ing and outside the ing? magnetic field intensit of a tooidal solenoid is given b N I H (inside ing) H = 0 (outside ing) 7. What is the significance of eneg densit? It depends on what factos? It indicates the amount of eneg stoed/unit volume of a sstem (electic o magnetic). Moe is the eneg densit moe will be the wok done fo the given volume. It depends on the medium fo the given field (Electic E o Magnetic H)

15 8. What is solenoid? An inducto coil consisting of multiple tuns of wie wound in a helical geomet aound a clindical coe is called as solenoid. 9.Give the epession fo inductance of a solenoid. N A 0 L l Whee, N -- is numbe of tuns. A -- is aea of coss-section. l -- is length of solenoid. --is fee space 0 pemeabilit 0. Distinguish between solenoid and tooid. Solenoid is a clindicall shaped coil consisting of a lage numbe of closel spaced tuns of insulated wie wound usuall on a non-magnetic fame. If a long, slende solenoid is bent into the fom of a ing and theeb closed on itself, it becomes tooid.. PART B a) An Ion ing with a coss sectional aea of 3cm and a mean cicumfeence of 5cm is wound with 50 tuns of wie caing a cuent of 0.3A. The elative pemeabilit of the ing is 500. Calculate the flu established in the ing. b) Region, 0 z m is occupied b an infinite slab of pemeable mateial(. 5 ).If B = 0a 5a m wb/m within the slab, detemine: i. J ii. J b iii. M iv. K b on z=0. a) The -plane seves as the inteface between two diffeent media. Medium (z < 0) is filled with a mateial whose 6, and medium (z > 0) is filled with a mateial whose 4. If the inteface caies cuent a m A/m, and B = 5a + 8a z m wb/m, find H and B o b) A small cuent loop L with magnetic moment 5a z A.m is located at the oigin while anothe small loop cuent L with magnetic moment 3a A.m is located at (4,-3,0). Detemine the toque on L a) Establish the elation of foce between cuent caing paallel conductos. b) Obtain the magnetic flu densit on the ais of a cicula coil caing cuent I. a) Deive an epession fo inductance of a solenoid with N tuns and l mete length caing of I ampees. b) Deduce the epession to find the magnetic field intensit H at an point P due to an infinite filamentat cuent caing conducto lies in Z-ais and caing I ampee. a) State and Eplain Ampee s cicuital law, Biot Savat law. b) State and Eplain Loent s Law

16 EE 630 ELECTROMAGNETIC THEORY UNIT-IV ELECTRODYNAMIC FIELDS PART A. State Faada s law of induction.. State lenz s law 3. Give the equation of tansfome emf 4. What is motional electic field? 5. What is motinal emf? 6. What is the emf poduced b moving loop in time vaing field? 7. What is time hamonic field? 8. Give time hamonic mawell s equation in point fom. assume time facto e -jωt 9. Distingush between Field theo and Cicuit theo 0. Wite Mawell s equation in point and integal fom fo good conductos.. What Is significance of displacement cuent densit?. In a mateial fo which σ= 5s/m and ξ= and E=50 sin 0 0t (V/m) find the conduction and displacement cuent densities. PART- B. What ae the diffeent was of EMF geneation? Eplain with the govening equations and suitable pactical eamples. (6). With necessa eplanation, deive the Mawell s equation in diffeential and integal foms (6) 3. What do ou mean b displacement cuent? wite down the epession fo the total cuent densit (8) 4.(a) Find the total cuent in a cicula conducto of adius 4mm if the cuent densit vaies accoding to J=0 4 /R A/m. (8) (b) Given the conduction cuent densit in a loss dielectic as Jc=0.0 sin 0 9 t A/m.find the displacement cuent densit if σ=0 3 mho/m and ξ=6.5 (8) 5 (a) Eplain the elation between field theo and cicuit theo. (8) (b)the magnetic field intensit in fee space is given as H=H 0 sinθa t A/m. whee θ=ωt-βz and β is a constant quantit. Detemine the displacement cuent densit. (8) 6 (a) Wite shot notes on faadas law of electomagnetic induction. (8) (b) Show that the atio of the amplitudes of the conduction cuent densit and displacement cuent densit is σ/ωξ, fo the applied field amplitude atio if the applied field is E=Em e -t/λ whee λ is eal. (8) 7. Deive Geneal field elation fo time vaing electic and magnetic fields using Mawell s equations. (6)

17 EE 630 ELECTROMAGNETIC THEORY UNIT-V ELECTROMAGNETIC WAVES PART A. What is wave? If a phsical phenomenon that occus at one place at a given time is epoduced at othe places at late times, the time dela being popotional to the space sepaation fom the fist location, then the goup of phenomena constitute a wave.. Give the wave equation in tems of electic field and magnetic field. The electomagnetic wave equation in tems of electic field is, E E E 0 t t The electomagnetic wave equation in tems of magnetic field is, H H H 0 t t 3. Give the wave equation in fee space. E t H t The wave equation in fee space in tems of electic field is, E 0 The wave equation in fee space in tems of magnetic field is, H 0 4. List out the popeties of a unifom plane wave. If the plane of wave is the same fo all points on a plane suface, it is called plane wave. If the amplitude is also constant in a plane wave, it is called unifom plane wave. The popeties of unifom plane waves ae: a) At eve point in space, E and H ae pependicula to each othe and to the diection of tavel. b) The fields va with time at the same fequenc, evewhee in space. c) Each field has the same diection, magnitudes and phase at eve point in an plane pependicula to the diection of wave tavel. 5. Give the epession fo the chaacteistic impedance of the wave. The chaacteistic impedance o intinsic impedance is the atio of the electic field intensit to the magnetic field intensit. E H of the medium. whee, 6. What is Vecto Helmholtz equation. is the pemeabilit of the medium and ε is the pemittivit The wave equation in lossless medium in phaso fom is called the vecto Helmholtz equation. E E 0 7. Give the wave equation fo a conducting medium. The wave equation fo a conducting medium in phaso fom is given as, E j j ) E 0

18 8. What is skin effect and skin depth? In a good conducto the wave is attenuated as it pogesses. At highe fequencies the ate of attenuation is ve lage, and the wave ma penetate onl a ve shot distance befoe being educed to a small value. This effect is called skin effect. The skin depth () is defined as that depth in which the wave has been attenuated to /e o appoimatel 37% of its oiginal value. It is also known as depth of penetation. whee, is the attenuation constant, 9. Give the epession fo attenuation constant and phase shift constant fo a wave popagating in a conducting medium. The attenuation constant fo a wave popagating in a conducting medium is, The phase shift constant fo a wave popagating in a conducting medium is, 0. Give the epession fo the velocit of popagation of a wave in an medium. The velocit of popagation of a wave in an medium is v whee, is the angula velocit and is the phase shift.. Define pointing theoem. The vecto poduct of electic field intensit and magnetic field intensit at an point is a measue of the ate of eneg flow pe unit aea at that point. P E H. What is Bewste angle? Bewste angle is an incident angle at which thee is no eflected wave fo paallel polaized wave. tan Whee is dielectic constant of medium is dielectic constant of medium 3. State one dimensional wave equation. E t E

19 4. What is the velocit of electomagnetic wave in fee space and in lossless dielectic. v 0 0 c m/s 5. Repesent equation of electomagnetic wave in the phaso fom. Wave equation in phaso fom is E E j E 0 O E E 0 Whee j ( j ) 6. Fo a loss dielectic mateial having, 48, 0s / m. Calculate the popagation constant at a fequenc of 6GHZ. Given data: 48 0s / m. f = 6MHZ Find: popagation constant ( ) Fomula: j( j ) Soluation:.3 j ( j ) j ( j.3) = j 5668 = = Result: = Bief about the intinsic impedance fo a pefect dielectic medium. Intinsic impedance fo a pefect dielectic medium is given b j je E Ω is a eal positive, Phase angle is zeo, Fo a pefect dielectic, both the field E and H ae in phase. 8. Bief about comple pointing vecto. The comple pointing vecto is given b P = ½ E H Poduct of E and H is a vecto poduct. Mutuall pependicula components of E and H contibute to the powe flow. This powe flow is diected along the nomal to the plane containing E and H.

20 9. What is mean b Linea polaization? The electic field E is the esultant of E X and E Y, and the diection of it depends on the elative magnitude of E X and E Y. The angle made b E with ais is given b tan E E If the esultant E is oiented in a diection which is constant with time, the wave is said to be lineal polaized. 0. State Snell s Law. When a wave is tavelling fom one medium to anothe medium, the angle of incidence is elated to angle of eflection as follows. sin sin i t PART B. a) A plane wave popagating though a medium with = 8, = has z / 3 8 E 0.5e sin ( 0 t z) a. V / m. and H field. Detemine, Wave velocit, The loss tangent, intinsic impedance b) deive the geneal electomagnetic wave equation.. a) Fo a paallel polaized wave, eplain cleal about Snell s Law and citical angle. b) Sea wate plas a vital ole in the stud of submaine communications. Assuming that fo seawate = 4 S/m, = 80, = and f= 00 MHz.Calculate a) The phase velocit b) The wavelength c) The skin depth d) The intinsic impedance a)an electic field in fee space is given b E 50cos ( t ). V /. Find the diection of the wave popagation, calculate phase constant and the time taken to tavel a distance of /. b) Pove pointing theoem a 0 m 4. a)a loss mateial has = 5, =. If at 5MHZ,the phase constant is 0 ed/m. calculate the loss tangent, the pemittivit, the attenuation constant and the intinsic impedance. b) Fo a paallel polaized wave, eplain cleal about Snell s Law and citical angle. 5. a) Eplain the wave popagation in loss dielectics. b) Define the tems: intinsic impedence, popagation constant, election and efaction coefficients.