An intensity current I descends down the $z$-axis from $z = \infty$ to $z = 0$, where it spreads out in an isotropic way on the plane $z = 0$. Compute the magnetic field.
To begin this problem I decided to break it into two problems. One where I solve for the magnetic field due to the wire and where I solve for the magnetic field due to the plane and add the two together for the total magnetic field. The magnetic field due to the wire is just half that of the magnetic field due to the infinite wire. So that $\vec{B} = \frac{\mu_0 I}{4\pi s} \hat{\phi}$, but I'm not sure if this works in all of space. For instnace, below $z=0$ the field would be a bit weirder I think.
The second thing I'm not sure about is how I compute the field due to the plane. I'm not sure what kind of loop to choose to make the problem easier. I think that the current surface density would be $\vec{K} = \frac{I}{r^2} \hat{r}$ so that it is isotropic and falls off as $r^2$