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What physical situation creates such a B field?

  1. Dec 6, 2017 #1
    1. The problem statement, all variables and given/known data
    We are given that the B-field is:
    $${\bf{B}} = C \delta(s-R) \hat{\phi}$$

    where ##s## is the distance from some object and ##R## is the radius of some object. What kind of physical situation would create such a B-field?

    2. Relevant equations
    Stated above.

    3. The attempt at a solution

    This is a tough question because it really involves creativity more than anything else. A "toroidal coil" creates a B-field that points in ##\hat{\phi}## and is constant but even if you figure out a clever way of canceling out the B-field in all but one location, how can you make it "infinite" at ##s = R##?

    Electric monopoles are usually characterized by the ##\delta## function, but magnetic monopoles don't exist so I can't really extend that analogy any further!
     
  2. jcsd
  3. Dec 6, 2017 #2
    But magnetic dipoles do exist. Think about what happens as you make a dipole smaller and smaller. What function would describe an infinitely small dipole?

    EDIT: Looking at the equation itself a bit more carefully, ##\mathbf{B}## is nonzero along a ring of radius ##R## (assuming cylindrical coordinates) and zero everywhere else. I don't know what physical situation would produce this but you can picture it as a single circular magnetic field line at ##R##.
     
    Last edited: Dec 6, 2017
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