推 dw1293 :推原PO電機系草，電子學型男 06/21 20:09
課程名稱︰電磁學一
課程性質︰必修
課程教師︰共同授課
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰2013/6/21
考試時限（分鐘）：10:20~12:10
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.(1) Write down the Maxwell equations in differential form.(2) Assume that
the sources and constitutive relations are given in solving an electro-
magnetic problem. Compare the number of unknown field quantities with that
of independent field equations. Are they equal or unequal? Explain briefly.
(16%)
2.(1) Consider a volume V enclosed by a surface S. Write down the Poynting
theorem for relating various energy components within V and on S. Also
describebriefly the physical meaning of each term in the theorem. (2) To
compute the time-average Poynting vector, we uaually introduce a complex
Poynting vector. Please write down the expression of that complex Poynting
vector. Is it a phasor? Explain briefly.(16%)
3.An infinite plane sheet lying in the z=0 plane carries a time varying
_ _
surface current of density Js=0.2cos(6π*10^8t=π/3)ay A/m. The region z>0
is a perfect dielectric ofε=2.25ε0 and μ=μ0, whereas the region z<0 is a
_
perfect dielectric ofε=4ε0 and μ=μ0.(1) Find the electric field E(z,t)
_
and the magnetic field H(z,t) in both regions z>0 and z<0.(2) Find the
_
polarization current density Jp(z,t) in region z>0. (24%)
4.(1) Write down the expressions for the electric field E(r,t) and the
magnetic flux density B(r,t) in terms of the electric scalar potential
Ф(r,t) and the magnetic vector potential A(r,t). (2) Now we make new
potential functions: A'=A+▽φ and Ф'= Ф-dφ/dt(偏微分), where φ is an
arbitrary scalar field. Show that the electric and magnetic fields are
unchanged in terms of these new potential functions. Discuss the physical
meaning of this result. (14%)
5.In a region with a nonuniform electrostatic field E(r), there is a small
dielectric object situated at point r0. By using the concept of the
polarization surface charge induced on a small dieletric object, show
qualitatively that the magnitude of the electric force on that small
dielectric object is approcimately proportional to |▽[|E(r)|^2]| evaluated
at r0. (9%)
6.Shown in the following figure are two concintric spherical perfectly-
conducting shells of radii a and c(a<c). Assume that the thickness of the
conducting shells is negligible. The space between conducting shells is
filled concentrically with two lossy dielectric whose conductivity and
permittivity are (σ1,ε1) for a<r<b and (σ2,ε2) for b<r<c, respectively.
the inner(outer) conducting shell is maintained at potential V1(V2). Find (1)
the steady current I flowing from the inner conducting shell to the outer
one, and (2) the surface density of free charges at the interface (r=b) of
two dielectrics, (3) Assuming that σ2=0 but σ1>0, find the current and the
potential V at r=b. (21%)
圖為三同心圓，由內到外半徑分別為a,b,c
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※ 編輯: sionchen 來自: 140.112.218.163 (06/21 14:03)