作者kagato (包)
看板Grad-ProbAsk
标题Re: [理工] [电磁]-云科90-电资所
时间Thu Jan 7 01:53:51 2010
※ 引述《aacvbn ( 姿势+)》之铭言：
: http://www.lib.yuntech.edu.tw/exam_new/90/el.pdf
: 第14页第2题 有附图@@
: The insulator between the inner conducting cylinder a and outer
: cylindrical shell b is composed of four sectors of equal
: dimensions but different dielectric constants,
: ε_1 ε_2 ε_3 and ε_4 ,see Fig.2. The radius of cylinder a is (r_a)
: and the inner radius of outer cylindrical shell b is (r_b).
: In case the cylinders extend indefinitely ,
: find the capacitance per unit length.
令中央带电+ρ_L , 外围带电-ρ_L
由Maxwell-equation ∫Dds = ρ_L → (D1+D2+D3+D4)*2πr/4 = ρ_L
ε1E+ε2E+ε3E+ε4E = 2ρ_L/πr , E = 2ρ_L/[πr(ε1+ε2+ε3+ε4)]
2ρ_L*ln(b/a)
V = ∫Edr = ____________________
[π(ε1+ε2+ε3+ε4)]
π(ε1+ε2+ε3+ε4)
C=ρ_L/V = _____________________ (F/m)
2ln(b/a)
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