# Net bound current with uniform magnetization

My confusion stems from the following:

Can I reason the answer being (D) analogous to... for instance:

If this was instead a solid cylinder with uniform polarization $$\mathbf P$$ pointing in the z-direction, I'd believe the net bound charge would be on the top/bottom surface only. That's because the constituents atoms in the volume will have their electron clouds and nuclei polarize along an external electric field such that the nuclei will tend to move towards the 'tails' of vector field $$\mathbf P$$ and the electron clouds away from it. For each electron cloud, there will thus be a neighboring nuclei canceling out its bound charge contribution, except at the top/bottom surfaces where there can be no neighboring charge for the bound charges there.

Can I apply this logic here? I also feel like my explanation was a bit confused or muddy.

$$\mathbf{M}=\alpha\mathbf{\hat{z}}H\left(1-\rho/R\right)$$, where $$\alpha$$ is a constant with suitable units, $$R$$ is the radius of you cyllinder, $$\rho$$ is the radial coordinate in Cyllindrical coordinate system $$\left(\rho,\phi,z\right)$$ and $$H$$ is the Heaviside step function (https://en.wikipedia.org/wiki/Heaviside_step_function).
Now simply take the curel, in cyllindrical coordinates (bearing in mind that $$\partial_\rho H\left(1-\rho/R\right)=\frac{-1}{R}\delta\left(1-\rho/R\right)$$) and find out what the current density is (it will be only around the edge).
Making use of Griffith's Introduction to Electrodynamics (4th Edit) $$\S 6.2.2$$: For the case of uniform magnetization with the dipoles represented by tiny current loops, the "internal" currents cancel: For every current loop there is a contingous loop where the current goes in the opposite direction. It is only at the bounding surface that this cancellation does not occur, leaving an effective current on the boundary: "It is a peculiar kind of current in the sense that no single charge makes the whole trip, each charge moves only in a tiny little loop .... Nevertheless, the net effect is a macroscopic current".