[積分] Flux
Find the flux of the curl of field F through the shell S
Q1..
F = 4zi - 7xj + 3yk ;
S: r(r,θ) = r cosθi + r sinθj + 6rk,
0 ≦ r ≦ 6 and 0 ≦θ≦ 2π
Q2..
F = 4(x^2)yi - 4x(y^2)j + ln(z)k ;
S: r(r,θ) = r cosθi + r sinθj + 3rk,
0 ≦ r ≦ 3 and 0 ≦θ≦ 2π
小弟做法如下..
Ans1..
curlF = ▽xf = 3i + 4j - 7k
n dσ = r x r dr dθ
r θ
flux = ∫∫(curlF)．(r x r) drdθ
r θ
= -252π
Ans2..
curlF = ▽xf = -4( x^2 + y^2) k
n dσ = r x r dr dθ
r θ
flux = ∫∫(curlF)．(r x r) drdθ
r θ
= 162π
以下為答案
A1: 252π
A2: 162π
想請問步驟在哪邊出了問題?? (求法向量的地方有未考慮到的嗎??)
謝謝 ╭(─╴╴─)╮ ▃▇
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◆ From: 140.115.213.119
※ 編輯: violet90079 來自: 140.115.213.119 (06/23 16:58)
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