Question

3. Consider TEM wave propagation in dry earth the relevant parameters are more and 0-10-*S/m. Answer the following questions using He = 4 x 10-7 H/m and if and when needed: a) (7 pts) For the TEM wave wavenumber 3 is much smaller than the damping constant a when the frequency : > 100 MHz - POSSIBLE or NOT POSSIBLE? Circle one and explain your answer b) (pts) Frequency is such that o >> we while 26 - POSSIBLE or NOT POSSIBLE? Circle one and explain your answer. c) (7 pts) If / - 100 Hz what is the wavelength A? d) (4 pts) 1 / - 100 Hz what is the penetration depth 8.

Answer 1

Wave propagating earth- (3) Solano Given that - TEM in dry M. = Mo = 47X102 H/m 8.85 X 10-12 E - Eo = welt 6= 10-3 m/s () for TEM Wave 6. where w = 2x 3.14 x 100 x 10 En gold wave number ß= SHE 22f 6. 28 x 108 uz rad = 6.28 x 108mad / see B = 6.28 x 108 x 4xx107x 8.85x10-12 = eap ß = 20.83 m 1 f 100 miz ; ß» 20. 83 met damping constant & & V H 10-3 २ 42x10-7 8.25X1012 d = 1.88 x 10 3x102 0.188 ml at f = 100 miz fuorul BY & ß>>. for f 77100 Euw

gt meand the given statment ģ meand the given stutment is not possible. (۵) the spin depth s for good conductor equal to the B. inverse the wave number gt mean 27 BE 27 11 S for good conductor 6» WE for given f 키 WE = 6.26410 x 8.85X10-12 w to = we = 3.56010- Sym this the and 10-3 meant 6 L ع نیا gt med hot given statment in possible.

(c) Solyn-g- ast = f Lootz then warelength d = . wgolxo.E f 3- 0x10 8 m/sec 100 // sec ) Lootz penetration depth (d) fa 3.0x106 27 2X3.14 6-1 4.78 x 10 = 4.78x10fmeter, SE