课程名称︰电磁学I 课程性质︰必修 课程教师︰张宏钧 江衍伟 林怡成 林晃岩 开课学院：电机资讯学院 开课系所︰电机工程学系 考试日期（年月日）︰2010/6/25 考试时限（分钟）：110分钟 是否需发放奖励金：是，谢谢 （如未明确表示，则不予发放） 试题 : 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 为x方向单位向量) 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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