課程名稱︰電磁學I 課程性質︰必修 課程教師︰張宏鈞 江衍偉 林怡成 林晃巖 開課學院：電機資訊學院 開課系所︰電機工程學系 考試日期（年月日）︰2010/6/25 考試時限（分鐘）：110分鐘 是否需發放獎勵金：是，謝謝 （如未明確表示，則不予發放） 試題 : 1. In Fig.1, media 1 and 3 extend to infinity, and medium 2 is a dispersive ( i.e., the material parameters depend on frequency) slab. For an infinite planar sheet current, lying in z=0 plane, J_s(t) = -2J_s0[cos(1.5x10^8πt]^2 ax A/m, (ax 為x方向單位向量) there will be electric and magnetic fields in the three media. The frequency dependency of material parameters of medium 2 are listed in the following Table 1 ┌───────┬─────┬─────┐ │ │ε(ω) │μ(ω) │ ├───────┼─────┼─────┤ │ω=0 │2ε0 │2μ0 │ ├───────┼─────┼─────┤ │ω=1.5x10^8π │2.5ε0 │2.5μ0 │ ├───────┼─────┼─────┤ │ω=3x10^8π │3ε0 │3ε0 │ └───────┴─────┴─────┘ (1) Can you solve the problem by using integral form Maxwell equations? Why? (10％) (2) Can you solve the problem by using time-dependent and differential form Maxwell equations? Why? (10％) (3) Please find the time-dependent form electric- and magnetic fields in all three media. (15％) (4) Please find the time-dependent form surface current on the surface of media 3. (5％) (5) Please find the time-average Poynting vectors in media 1 and 2 and explain the physical meaning of the results briefly. (10％) Medium 1 │ Medium 2 │ Medium 3 │ │ x (μ0,ε0) │ (μ(ω),ε(ω)) │ PEC(σ=∞) ↑ │ │ │ J_s(t)↓ │ │ z=0 z=1/6 m y⊕──→z Fig. 1 for Problem 1 2. The space between two parallel conducting plates each having an area S filled with two different lossy dielectrics as shown in Fig.2 ,where the thicknesses d1,d2 << S^(1/2) = L (the length) so that the fringe effect can be neglected. A battery of dc voltage V is applied across the plates. Please determine (1) The steady current densities in both dielectrics. (10％) (2) The electric field intensities in both dielectris. (10％) (3) The surface charge densities on the plates and the interface. Please explain briefly the reason of the existence of the surface charge density on the interface. (10％) (4) If the steady magnetic field is neglected, please draw the equilivalent circuit of this system and show the circuit parameters. (10％) (5) The power dissipation in this structure. (10％) L ▅▅▅▅▅▅▅▅▅▅▅▅───┐ d1│ε1,σ1,μ1 │ │V x ├───────────┤ ─┴─ ↑ │ │ ┬ │ d2│ε2,σ2,μ2 │ │ │ │ │ │ z←──⊕y ▃▃▃▃▃▃▃▃▃▃▃▃───┘ Fig.2 for Problem 2 --

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