桀特 發問時間: 科學其他:科學 · 9 年前

大學物理~電容 急!!

1.An air capacitor is formed from two long conducting cylindrical shell which is coaxial, and have radii of 13mm and 85mm. The eletric potential of the inner conductor with respect to the outer condutor is -600V. The maximum energy density of the capacitor in J/m^3

is closest to Answer: 2.7*10^-32.A 1m long piece of coaxial cable has a wire with a radius of 1.1mm and a concentric conductor with inner radius 1.3mm. If the voltage drop is 6000V, and the line charge density X ,is 8.8*10^-6/m, find the value of dielectric constantAnswer: 4.43.A 9*10^-6 C point charge is located at the origin.How much energy does its electric field store outside a sphere centered about the origin with a radius of 5 mm?Answer: 73J

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需要詳細的算式~! 拜託各位了!!

2 個已更新項目:

So the energy is:

0.5 x (9 x 10-6)2/(5.561 x 10-13) = 73 J

可以詳細說明一下原因嗎?? 謝謝...

2 個解答

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  • 最佳解答

    1) The shunt capacitance of the coaxial cylinders is:

    2πε/ln (D/d)

    = (2π x 8.85 x 10-12)/ln (85/13)

    = 2.961 x 10-11 F/m

    So in 1 m long of the cable, its capacitance is 2.961 x 10-11 F, with energy stored = 0.5 x 2.961 x 10-11 x 6002 = 5.33 x 10-6 J

    And the volume of the capacitor is:

    1 x π(0.0852 - 0.0132) = 0.02217 m3

    Hence energy density is (5.33 x 10-6)/0.02217 = 2.7 x 10-3 J/m3

    2) The capacitance of the cable is:

    C = 2πε/ln (1.3/1.1) where is the permittivity of the capacitance.

    Also, charge stored = 8.8 x 10-6 C

    So capacitance = (8.8 x 10-6)/6000 = 1.467 x 10-9 F

    Now we have:

    2πε/ln (1.3/1.1) = 1.467 x 10-9

    ε = 3.899 x 10-11 F/m

    So the dielectric constant is (3.899 x 10-11)/(8.85 x 10-12) = 4.4

    3) Capacitance of the sphere = 4πεr = 4π x 8.85 x 10-12 x 0.005 = 5.561 x 10-13 F

    So the energy is:

    0.5 x (9 x 10-6)2/(5.561 x 10-13) = 73 J

    2011-12-14 08:35:13 補充:

    在 capacitor 中, stored energy 的 formula 為

    CV^2/2 或 Q^2/(2C)

    此處我用了後者

    參考資料: 原創答案
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  • heaven
    Lv 6
    9 年前

    風卷 good

    ....

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