[電磁] question

[unknown1 (unknown1)]

請問一下~
a long cylinder carries a charge density that is proportional to the distancefrom the axis: p=ks, for some constant k.
Find the electric field inside this cylinder

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作者: bzvxc ( ) 看板: TransPhys
標題: Re: [電磁] question
時間: Mon Jul 18 01:02:38 2005

※ 引述《unknown1 (unknown1)》之銘言：
: 請問一下~
: a long cylinder carries a charge density that is proportional to the distance
: from the axis: p=ks, for some constant k.
: Find the electric field inside this cylinder

Assume that the cylinder has radius a.
 │
a├───────────
 │          r ' ←point q
 ───────'───────>
 │            z                z'
a├───────────
 │

       1        p
E(q)=── ∫  ── dv
     4πε  v' R^2
       1   s a   kz         2π
    =── ∫∫────rdrdz∫ dφ
     4πε 0 0 z^2+r^2      0
      k
    =─ (s^2+a^2)*Ln(1+(a/s)^2) ...ans
     8ε

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