課程名稱︰電磁學二 課程性質︰物理系必修 課程教師︰賀培銘 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2011-04-21 考試時限（分鐘）：180分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.(10%) Write down all Maxwell equations with source terms in vacuum. 2.(10%) (1) Compute the self-inductance of the "hairpin" loop shown below. (Neglect the contribution from the ends; most of the flux comes from the long straight section.) Assume that the wire has a tiny radius ε, and ignore any flux through the wire itself. (2) Find the total energy of the system when the current I on the loop is given. ╭───────────────────╮ ┬ │ │ │ d ╰────● ●────────────╯ ┴ ├───────────────────┤ l → ^ 3.(20%) Two parallel straight wires with the same current I =Iz are located at (x,y)=(0,-d/2) , (0,d/2). (a) Find Maxwell stress tensor on x-z plane at y=0. (b) Compute the integral of the Maxwell sterss tensor over x-z plane at y=0. (Integrate along the x direction only.) (c) Note that the x-z plane is not a closed surface. Comment on why (or why not) (b) gives the force of a current I on the other. 4.(15%) Concentric spherical conducting shell of radii a and b (b > a) with charges Q and -Q, respectively, are placed in the background of a uniform → ^ magnetic field Ｂ= B0ｚ. Find (1) the linear momentum of the system, and (2) the angular momentum of the system. 5.(25%) Consider the incidence of a monochromatic plane wave with the electric field given by → ^ ik1(zcosθI+xsinθI) -iωt EI = y EI0．e ．e ( z < 0 ) at the interface of two linear media at z=0. The media for z < 0 is an insulator with the permittivity ε1 and permeability μ1. The media for z > 0 is a conductor with conductivity σ and its permittivity and permeability are ε2,μ2. We expect the transmitted wave to be of this form → ^ -κz ik2(zcosθT+xsinθT) -iωt ET = y ET0．e ．e ．e ( z > 0 ) (a) Find κ and k2 (in terms of ε1,ε2,μ1,μ2,σandω). (b) Find θT. (You can use k1,κ,k2 andθI to express θT). (c) Find ET0. (You can use k1,k2,μ1,μ2,κ,θI,θT and ω to express your answer.) 6.(20%) Which of the following is (are) correct? (a) Even static electric and magnetic field background can carry linear momentum. (b) For a monochromatic plane wave in vacuum, the energy density in the electric field is always that same as the energy density in the magnetic field. (c) The intensity of an EM wave is defined as the time-averaged power per unit area transportes by the EM wave. (d) Brewster's angle refers to the angle of the incidence at which there is no transmission. (e) Total reflection is possible only when the index of refraction of the medium in which EM waves propagates is smaller than that of surrounding medium. (f) If the group velocity is larger than the velocity of light in vacuum, causality must be violated. (g) The phase velocity is always larger than the group velocity. (h) It is impossible for the TEM mode to propagatr in a coaxial to [LC]^(1/2) (j) The energy density in the electric field is given by (ε0．E^2)/2 only when the electric field is static. --

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