課程名稱：電磁學上
課程性質：物理系必帶
課程教師：王立民
開課學院：理學院
開課系所：物理系
考試日期（年/月/日）：99/10/21
考試時限（分鐘）：120分鐘（8:10~10:10）
是否需發放獎勵金：是
範圍：Introduction to Electrodynamics 3rd edition CH1~CH2.4
1.Assume a vector function v=(x^2*y)i + (-x*y^2)j. Test Stokes' theorem:
(a)Find ∮v．dl around the triangular contour shown in Fig.1.(10%)
(b)Evaluate ∫(▽×v)．da over the triangular area.(10%)
↑
│ ．(1,2)
│ ↗│ Fig.2 為一半徑r=1，球心(0,0,0)
│ ╱ │ 的半球面在z>0的部分
│ ╱ │
│ ╱ │
│╱ ↓
┼←────┴───→
│(0,0) (1,0)
Fig.1
2.A vector field D=[r(cosψ)^2] r(unit radius vector) exists in the region
over the hemisphere with radius of r=1 as shown in Fig.2. For checking the
divergence theorem, evaluate:
(a)∮D．da (10%)
(b)∫(▽．D)dτ (10%)
1 δ 1 δ 1 δ(Dψ)
▽．D=── ──(r^2*Dr)+──── ──(sinθ*Dθ)+──── ───
r^2 δr r*sinθ δθ r*sinθ δψ (δ:偏微分)
3.A spherical distribution of charge ρ=ρ0*(1-r/b) exist in the region
0<=r<=b, where ρ0 and b are constant. Determine:
(a)The total charge Q.(5%)
(b)Electric field Einside and Eoutside.(5%)
(c)Electric potentials Vinside and Voutside.(5%)
(d)Electrostatic energy W stored.(5%)
4.A uniformly charged sphere of radii R centered at the origin (point A)
has a spherical cavity of radii R/2 centered at (x=R/2,y=0,z=0). The total
charge of the solid part is Q.
(a)Find the electric field E for any point in the cavity.(10%)
(b)Calculate the potential difference between point A and B, where point
B is at (x=R,y=0,z=0).(10%)
5.A long coaxial cable (Fig.4) carries a uniform nolume positive charge
density ρ on the inner cylinder (radius a), and a uniform negative surface
charge density on the outer cylindrical shell (radius b). The cable is
electrically neutral.
(a)Find the potential difference between a point on the axis and a point
on the outer cylindrical shell.(10%)
(b)Calculate the energy per unit length of this configuration.(10%)
Fig.4 有一內半徑為a的帶正電實心圓柱，外面包著外半徑為b的帶負電圓柱形薄殼。
6.Consider two concentric spherical shells, of radii a and b. Suppose the
inner one carries a charge 2q, and the outer one a charge -q (both uniformly
distributed).Calculate the energy of this configuration in two different
ways.(20%)
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※ 編輯: jipq6175 來自: 61.216.0.178 (11/20 18:00)