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Spherical Boundary Displace Current

  1. Nov 18, 2011 #1
    1. The problem statement, all variables and given/known data


    A current I is flowing along the y-axis and a
    spherical surface with radius 1 m has its center at
    origin, as in the figure left. A closed contour C is
    chosen as in the figure, which is a boundary
    between two semi-sphere surfaces S1 and S2. Based
    on the uniqueness of magnetic field circulation (Closed line integral of)
    H dot dl calculated from both surfaces S1 and S2,
    find the total displacement current emanating from
    the spherical surface using the Ampere’s law.

    2. Relevant equations

    No idea

    3. The attempt at a solution

    Not even sure where to start because it isn't clear whether these are conductive spheres or dielectric spheres. Once I figure that out, I could use the boundary conditions somehow... I honestly have no idea how to start this problem.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 19, 2011 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Well, maybe I can at least give you an idea or two.

    First, current i must be time-varying, or nothing happens electric-field-wise.

    Second: using Ampere, write an expression for B around the wire, including the space defined by the two hemispheres. BTW the hemispheres are just geometrically descriptive surfaces. They have no material meaning. Least that's what I assume.

    Third: now you have B(x,y,z). What is the Maxwell relation that relates E to B?

    Fourth: what is the relation between E and D? Assume non-conducting medium.

    Fifth: What is the meaning of "displacement current emanating from the spherical surface", given D and the surfaces? Think of an analogy with how you get from conduction current density J to conduction current in the Maxwell relation relating B to J and D.

    Sixth: how can you apply Stokes' theorem in conjunction with item 3 to calculate item five?

    No guarantees her, maybe you'll discover something along the way I didn't.
     
    Last edited: Nov 19, 2011
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