In the dielectric media with σ= 2.3 × 10" S/rm and & a. Obtain H(z,t) b....
8. In a lossless Eq, λ and H. dielectric for which η,:20π, μ.-1,and E(z,t) 94πcos(wt +2z) a/m. Calculate 9. A plane wave in a lossless medium has H(z,t) 0.2 cos(ot-62)-y 2 sin(ot -6z) AV/m. Find a) The direction of wave propagating. b) εr and a. c) E(z,t). 10. The electric field component of an electromagnetic wave in free-space is given by E.z,t)Eocos(ay)sin wt -kx) V/rm (Hint: Use the identity 2 sin a cos b (sina+ b) +sin(a -b)) a) Find...
8-16 Two nonmagnetic dielectrics( μ: 1 ) have the same dielectric constant( ε.-2.25 ), but different conductivities( σ-O and G-50 [S/m). If a wave of a frequency 100 MHz) propagates in each dielectric, compare the values of (a) β, (b) λ, and (c) up of the two waves. An electromagnetic plane wave propagating in a nonmagnetic dielectric has the instantaneous electric and magnetic field intensities given as 8-17 (z.t)- a,967.le" cos(1.5x10°t-Bz) and 'W(z, t) = ay 10e-az cos(1.5x10°t-Bz-0.7194) Determine (a)...
Problem 4: Time harmonic waves in lossy dielectric Start with Maxwell's equations and show that the electric field E(x, y, z, t) in a conductive material with conductivity σ satisfies the following wave equation a. 72 _ με.at? _ μσαί)F-0 b. Show that the following is a solution E(F, t)-(8 + 9) Eo e-kız cos(at-kez) where Eo is a constant and kR and k, are given by 0.5 w22 c. Obtain the direction of propagation for the wave in part...
A uniform plane wave in a lossy nonmagnetic medium of dielectric constant &2.3 is described by 0s t-3.40a, v/m. E(z,t)-1 0e-02: cos(9% 108 t _ 3. 4z)a, +24e cos(9x1 (a) (b) (c) Calculate the intrinsic impedance n. (3 marks) Determine H(z,t). (1 marks) Find the displacement current density Ja (3 marks)
1. Consider the Partial Differential Equation ot u(0,t) = u(r, t) = 0 a(x, 0)-x (Y), sin (! We know the general solution to the Basic Heat Equation is u(z,t)-Σ b e ). n= 1 (b) Find the unique solution that satisfies the given initial condition ur, 0) -2. (Hint: bn is given by the Fourier Coefficients-f(z),sin(Y- UsefulFormulas/Facts for PDEs/Fourier Series 1)2 (TiT) » x sin aL(1)1 a24(부) (TiT) 1)+1 0 1. Consider the Partial Differential Equation ot u(0,t) =...
Problem (3): In a non-magnetized dielectric the plane wave H field is given by: H(z,t)-2ei(1.5x10%+10%) Amps/m Find an expression for E
4. (20 points) A wave is propagating in a lossy dielectric with ly = 1.6, Er = 4.3, and o = 0.019 S/m at a frequency f= 2.7 GHz. The phasor representation of E field is given by Exs = 610e j30º e-(a+jB)z V/m (a) Find a, b, a,v,n. (b) Find the phasor representation for H field, i.e., Hys. (c) Find the equation of E(z ,t). (d) Find the value of E(z, t) at z= 1.2m, t = 10 ns....
2. A lossy dielectric sphere of radius b+01 m. ErHP and σ-10, Sim is initially charged at t-o Assume the initial volume charge density is p,(c/m), rsb. Determine: a. The time dependent expression of the current density in the sphere. b. Stored electrostatic energy in the sphere at i 2ms Hint:e, -x10-9 F/m 36 π 2. A lossy dielectric sphere of radius b+01 m. ErHP and σ-10, Sim is initially charged at t-o Assume the initial volume charge density is...
Problem 6. Electromagnetic plane waves in a lossy medium The electric field of an electromagnetic plane wave traveling in a lossy medium can be written as where z is the distance, t is time, and fthe frequency. For f 1 GHz, it is found by measurement that the amplitude of the electric field is attenuated by a factor of 3 after the wave travels 100 m (i.e., to 1/3 of the amplitude at z-0 when it arrives at z- 100...
A parallel plate capacitor is composed of two lossy media with relative dielectric constant &ri 12 and 82 3.5, and thickness di 1.5mm and d 3.5mm. Lossy nature manifests itself through a steady-state leakage current with the normal component Jn flowing across the interface between the two dielectric media which have electrical conductivity o1 2x 10-3 and a2 = 5 x 104 S/m, respectively. The two media have dielectric strength EMaxt = 60 MV/m and EMax2 25 MV/m respectively, where...