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Homework Help: Magnetic flux density

  1. Apr 2, 2010 #1
    π²³ ∞ ° → ~ µ ρ σ τ ω ∑ … √ ∫ ≤ ≥ ± ∃ · θ φ ψ Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô
    1. The problem statement, all variables and given/known data
    An arbitrarily long hallow cylindrical electric conductor shown carries a static electric current density J=[tex]\hat{z}[/tex]J0. Determine the magnetic flux density B in the hallow region of radius a. Your result should show that B is constant in this region.


    2. Relevant equations
    ∫B.dl = µ0I


    3. The attempt at a solution

    current I = [tex]\hat{z}[/tex]J0pi(b2-a2)

    B. 2pia = µ0 [tex]\hat{z}[/tex]J0pi(b2-a2)

    B = µ0 [tex]\hat{z}[/tex]J0(b2-a2) /2a

    I am not sure about B.dl being B.2pi a
     

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    Last edited: Apr 2, 2010
  2. jcsd
  3. Apr 2, 2010 #2
    Utilize the relation

    [tex]\vec{B}=\frac{\mu_0\vec{J}\times\vec{r}}{2}[/tex]

    and approach the problem with a uniform current distribution throughout the circle of radius b, plus a current in the opposite direction in the hole.
     
  4. Apr 4, 2010 #3
    I am trying to do exactly that: +J current density in b and -J in region of radius a.
    Add both to get result. But in the equation you mentioned, how to calculate the cross product.
    seems a bit complicated. Can't I use just ∫B.dl = µ0I
     
  5. Apr 4, 2010 #4
    Superposition of B within the hollow region:

    [tex]\vec{B}=\vec{B_b}+\vec{B_a}[/tex]

    [tex]\vec{B}=\frac{\mu_0\vec{J}\times(\vec{r_b}-\vec{r_a})}{2}[/tex]

    So, what is

    [tex]\vec{r_b}-\vec{r_a}[/tex]

    equivalent to?
     
  6. Apr 5, 2010 #5
    ddddddddddddddddddddddddddddddd.
    Can't believe I missed it.
    I shall go shoot myself in the foot.

    Before I do that, can you tell me how to solve Jxr for a single sphere problem.
    Just do the cross product or is there some trick?
     
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