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Levitating wire in magnetic field.

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data
    A copper wire of diameter d carries a current density at the Earth’s equator where the Earth’s magnetic field is horizontal, points north, and has magnitude 5.yz × 10^-5 T . The wire lies in a plane that is parallel to the surface of the Earth and is oriented in the east west direction. The density and resistivity of copper are ρm = 8.9 × 10^3 kg/m3 and ρ = 1.7 × 10^−8 Ω-m, respectively. (x,y and z are given constants).

    (a) How large must J be, and which direction must it flow in order to levitate the wire? Use g= 9.81 m/s

    .(b) When the wire is floating, how much power will be dissipated per cubic meter due to resistive heating in the wire?

    2. Relevant equations
    F = ILB (F = JALB = JVB.)
    F = mg.
    m = density(Volume)
    So, F = density(volume)(g)
    3. The attempt at a solution
    JVB = density(V)(g)
    cancel the V's and solve for J (Positive so it flows in the east direction?)

    I think that's the correct way to do (a), please point out if I've made an error. I can't seem to find the relative equation for part (b). Any help would be great!
     
  2. jcsd
  3. Feb 23, 2013 #2
    Anyone have any clue? I can't see a way to do it without some extra numerical value for the dimensions of the wire.
     
  4. Feb 23, 2013 #3

    haruspex

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    The specific dimensions should cancel out. Create unknowns for cross-sectional area etc. as necessary and post you working.
     
  5. Feb 24, 2013 #4
    Well, I said that resistance = (resistivity x L) / A. Then JA = I. Power = (JA)^2 x (restivity x L) / A. This simplifies to be P = J^2 x resistivity x V. I don't know the value of V though. I'm not sure what way you had in mind. Any ideas?
     
  6. Feb 24, 2013 #5

    haruspex

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    You are not asked to find P. What does the question ask for?
     
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