# Homework Help: What physical situation creates such a B field?

1. Dec 6, 2017

### talrefae

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. Dec 6, 2017

### NFuller

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