What physical situation creates such a B field?

[member 545369]

Homework Statement

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?

Homework Equations

Stated above.

The Attempt at a Solution

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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!

 

[NFuller]

Electric monopoles are usually characterized by the δδ\delta function, but magnetic monopoles don't exist so I can't really extend that analogy any further!

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 $R$.