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chap10 014

# chap10 014 - 10.12 PROBLEMS 10.31 b Calculate the real and...

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Unformatted text preview: 10.12. PROBLEMS 10.31 b. Calculate the real and imaginary parts of the permittivity. Problem 10.26: From Section 10.7 we see that the electric ﬁeld of a plane wave penetrating (slightly) into a good conductor may be written in phasor notation as E = 1908— 13+. 2 where 6 = ('Ir}",u,oo)‘1/2 is the skin depth in the conductor. a. Show that the magnetic ﬁeld of this plane wave may be written in phasor form as H: Placid-51”"? wood b. Show that the integral from .2 = 20 to z = 00 of the ohmic (or Joule) heating per unit volume éiR {El - 3*} is equal to the time-averaged Poynting vector < 13 > at z = 29, Le, the incident and dissipated powers are equal. c. Express the ﬁelds given above as a function of space and time. (1. Calculate the time-averaged energy stored in the electric and magnetic ﬁelds for the example given above. Problem 10.27: A circularly polarized plane wave whose electric ﬁeld is given by E = Ego“: + me-ﬂm-kz) is propagating in a slightly lossy dielectric medium. The frequency of the wave is 1 GHz and the wavelength is measured and found to be 10 cm. The average power flux at z = 0 is 30 W/m2 and the wave is attenuated at a rate of 2 dB / m. a. Determine the complex permittivity of the medium. b. Calculate numerical values for E0, w, and the complex wavenumber k = k' — jk” in the above equation for the wave electric ﬁeld. c. Give a complete phasor description of the wave magnetic ﬁeld. Problem 10.28: The electric ﬁeld at the surface of a semi-inﬁnite slab of a good conductor having a conductivity 0’ is given in phasor form by the relation E 2 (f: + jy)Eoe-J‘(1+j)Z/5 a. What is the form of the ﬁeld E(z,t)? b. Use superposition or other means to calculate, in phasor form, the magnetic ﬁeld as a function of z. c. Calculate the time-averaged energy density stored in the electric and magnetic ﬁelds at a distance 2: into the conductor. ...
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