Question

03:15 points Answer brielly to each of the following questions (a) State the differential form of the continuity equation Derive the integral form of the continuity equation from its differential form. Identify all the quantities and indicate the units. () (b) What are the three constitutive relationships to characterize electrical media What is the difference between a linear and a non-linear medium? (2) (c) Starting from the time-harmonic form of Maxwell's equations, derive the wave equation for time- varying magnetic field (H) in a soure-free but lossy medium (4) (d) What kind of a wave (standing, travelling, direction) is represented by the following solution of the wave equation? Is this form of solution possible for naturally occurring medin? Answer with reasoning (3) h(2) = ne-ae2 (e) What is equivalent conductivity of a medium? What are its two components? Write their expressions and state the physical phenomena which are responsible for these components (3)

Answer 1

eg ut couternity from the principle of charge of charge must be aqual quén vollene to Combination the teine viate of decrease within the net autward current flow lliccough the flerface of flei_volume. I aut -dain at I= current du density J=1/5 sids f Jocs doin at divuyauct theosen II (V.J) di d Hll Pudu. VJ alu at continuity oqa J=6E V.GE olu alu at -I alu O(VE)= - osv (VE). D of 6 af. D.D= lv DE EE E DE su & DE Sule fu E -l alu 6 at -fv E al at alv fy 6.at E.

du lv et tkr E Etki K -4 te Su Su = Lv ste/6. e e e -after Svo e Tr= relaxation teine SE Cseegi elwegen deneily de material to drop to * Ive is the eintial el deneity Lilly Ly atteo Relaxation time ell the time it takes ela charge placed in the interior é' (361877' of its initial value. Sv = Svo e Svo *0.368 36.8 7. of Sve eindicates that evolume charge su ví a_muturiol dresy wypenentially for metals very hille kielice relaxatibu tire is very small flance charge deceys very soon. 6=5.8x107 Sim. Examples for copper spm Er = Relalation times 000100 pec 6?1017 syos for Quartz lontinuity is 1-8860-19 IN ک - بوع Top = 51.2 days

I -> wvient density (Aymy & voluine charge density (C/m3) 1 → curent (A). E + electric field Nim)

9 can characterize the relectical media in three ways as t. Capacitance CCT Vs frequency measurement charging profile over linu of cell free media, cell expressing viruses (WT) and cells alone (control) real part of impedance Vs measurement frequency

Linear medium free free of hysteresis free of source of saturation Non unear Saturation is present Hysteresis is present full Source

Tume Harmonic field to A teine harmonic field is one that varies pisiodically sinusoidally vary with Time j wt Ex. e sciuta ƏE jwe jo - jWE at ad jwo 241 It jwH. DXH = It OD Oto = 6E + 6 Ef IWD twee f6+ WEE DXH. XI

the klove_fropagation in loppy Lossy dulcebia es Cumperfect dielective on Conceder a liniar isotropic homogeneous lossy dielectric medium that u ch charge D.D = Su dieleetiuc s. partially conducting medlem imperfect conductor free (Lv 2000 ID 20 D.E FO

V.BO VH=0 TXE = - OBlat XE = .gmt tHitmfXA @ Hitant 3 PXH Jt 2D/at CE + WD: (0+WE)E VXH u cert of aq 3 Taking coerul VA EXE D(DoE) - DE TRE TRE THXAT html, THXD) nimf- Tantra ) nont 3 Com trendom 6 33m E D2E VE =l r= pscopagation Loutant AJP do attendew coustent: ( Nepoum m) ß= phase constant (read/m). I Nepes 8.68 dB = 20 logo raz wpl 6tJwe) ra fwilf otjwe) V = (01Jp)

dijs = jwplaf GtJwe). (01.jp) -joo je 65 ejuk) at 208j – p² = jwps - wipe - B ωμε. 2 9 WME. 20 B ~ - who. Wha 2B w . per content B? - Wu??.. When 2 4B اميره -44 4 B E, w & 4p2. 48* - 4pwue - w pi? D 4 HELH6B40*4*€ Holette 8 Wue I 18tween + w piase. a= W ME 2 Meny It ta 6 WE 13 WIDE #1 146 65 ß = It/6 WE 2.

roz Equation of E E to e de cos(wt - p2) 5x ãe xan ax.x ar = az ay ܛܘܿ lah # = Ha edz Costcent - p2) ay Eo V Ho A Vlm Alm Intrinsic Impedance: E Ho Patuwe ciupedance simpedance is the impedance offered by the medium. When the wave travels in a medima for Ingry medium- Joop 6+we.

. this form of solution is possible for naturally ocening media. apply this to shallow water egna can