field.and.wave.final.test
- 1. Right or Wrong 1. Static electric fields are solenoid, and static magnetic fields are irrotational. 2. Electromagnetic boundary conditions are derived by applying the integral form of Maxwell’s equa- tions to a small region at an interface of two media, and the tangential component of an electric field is discontinuous across an interface where a surface charge exists. 3. A linearly polarized plane wave can be resolved into a right-hand circularly polarized wave and a left-hand circularly polarized wave of equal amplitude. 4. The T E 11 mode is dominate mode of rectangular waveguide. 5. The group velocity is the velocity of propagation of an equiphase front, and the phase velocity is the velocity of propagation of the wave-packet envelope (of a group of frequencies). Fill the vacancies 1. Write the four Maxwell’s equations in differential form: . 2. It’s known that the propagation constant γ 2 = −ω 2 µϵc , where ϵc = ϵ − jσ/ω, so the attenuation constant α= , and the phase constant β= . 3. When we regard a conducting medium as a good conductor, on the contrary, if we will classify a medium to be a low-loss(good) dielectic.( Expressed by the relation of ω, σ and ϵ ) ⃗ 4. Poyting vector S is a power density vector associated with an electromagnetic field, and its ex- pression is ⃗ . The average power density Sav can be obtained by intergrating the instantaneous ⃗ over a fundamental period, and its expression is Poyting vetor S(t) . ⃗ 5.The electromagnetic force F acting on a point charge q with a velocity vector ⃗ due to the electro- υ magnetic fields is , which is called Lorentz’s force equation. Application 1. (10) A positive point charge Q is at the center of a spherical conducting shell of an inner radius ⃗ R0 . Determine E as funtions of the radial distance R. ( Apllying Gauss’s law ) ⃗ ⃗ 2. (16) A y-polarized uniform plane wave (Ei /Hi ) with frequency 300 (MHZ) propagates in air in the +x direction and impinges normally on a perfectly conducting plane at x = 0. Assuming the ⃗ amplitude of Ei to be 12 (mV/m), write the phasor and instantaneous expressions for a) E⃗ i and Hi of the incident wave. (4) ⃗ ⃗ ⃗ b) Er and Hr of the reflected wave. (4) c) E⃗1 and H1 of the total wave in air. (4) ⃗ d) the time average poyting vector in medium 1(see picture). (4) 3. (10) The electric field intensity of a linearly polarized uniform plane wave propagating in the ⃗ +y direction in sea water is E = αz 100 cos(107 ωt)(V /m) at y = 0. The constitutive parameters of ⃗ sea water are ϵr =72, µr = 1, and σ = 4(S/m) a) Determine sea water is low-loss dieletrics or good conductors? (2) b) Find the attenuation constant and skin depth. (4) ⃗ c) Find the distance at which the amplitude of E is 1% of its value at y = 0. (4) ⃗ 4. (16) The E field of a uniform plane wave propagating in a dielecric medium (µ = µ0 ) is given √ √ ⃗ 1 t) = αx cos(108 t − z/ 3) − αy sin(108 t − z/ 3)(V /m) by E(z ⃗ ⃗ a) Determine the frequency and wavelength of the plane wave; b) What is the dielectirc constant of the medium ϵ; b) Describe the polariztion of the wave. ⃗ d) Find the corresponding H field. 5.(16) A 2.5(cm)×1.5(cm) rectangular waveguide operating at 7.5 GHz. a) If the waveguide is filled with a dielectric medium characterized by ϵr = 2, µr = 1 and σ = 0, what modes can propagate in the waveguide? (8) b) If the wave guide is hollow, find the β, µg , λg and ZT E10 of the dominant mode T E10 . (8) 1