1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Attached Files:

    • 7.jpg
      File size:
      10.8 KB
    Last edited: Apr 2, 2010
  2. jcsd
  3. Apr 2, 2010 #2
    Utilize the relation


    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:



    So, what is


    equivalent to?
  6. Apr 5, 2010 #5
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook