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Line charge creating induced emf and displacement current

  1. Mar 31, 2016 #1
    1. The problem statement, all variables and given/known data
    A long, straight wire has a line charge, λ, that varies in time according to: λ = λ0 exp(-βt). A square wire loop of dimension a is located adjacent to the wire at a distance of a from the wire. Calculate expressions for the displacement current at the center of the wire loop and the magnetic flux through the loop.

    a = the side length of the square wire loop.
    λ0 = the initial charge of the line charge at time t = 0
    β = I assume some kind of constant. I haven't encountered this variable in a displacement current problem before.
    2. Relevant equations
    idisp = ε0 * dΦe/dt
    ε = -dΦm/dt
    Φm = ∫B ⋅ dA
    Φe = ∫E ⋅ dA = qenc / ∈0
    ∫ E ⋅ dl = -dΦm / dt

    3. The attempt at a solution
    I'm pretty sure I can find an expression for the electric field first by integrating the equation for the time-varying charge, but I'm not sure how to set that up. I think I should integrate with respect to time and treat radius as a constant. From the electric field I can use Faraday's Law to find the emf, but again I'm unsure as to how exactly to set up the math.
     
  2. jcsd
  3. Apr 1, 2016 #2

    rude man

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    What is the juxtaposition between the wire direction vector and the normal to the loop? I.e if the wire vector is in the x direction, is the loop normal in the y or the z direction?

    Is "a" the distance from the loop's center to the perpendicular distance to the wire, or is "a" the perpendicular distance from the closer collinear loop segment to the wire?

    A picture would help immensely.
     
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