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Suppose we have a short circular cylinder of radius $a$ and length $L$ carrying a uniform frozen-in’ magnetization $\mathbf{M}$ parallel to its axis.

Why is there no bound surface current on the two sides of the cylinder?

I understand that for a long circular cylinder, due to it being infinite, the direction of the magentic field is $\hat{\boldsymbol{\phi}}$ direction.

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This is regarding Problem 6.9 from Introduction to Electrodynamics by Griffiths where we need to find the magentic field due to polarization.

In the answers when finding the bound current it says

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  • $\begingroup$ hint: make a small rectangular loop whose "short" sides are parallel with and the "long" sides are perpendicular to $M$, resp.,; now calculate the circulation. $\endgroup$
    – hyportnex
    Jul 28, 2021 at 19:21

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There is a surface current resulting from the magnetisation, but using it to find the field is an alternative to using M. It's a choice between a macroscopic continuum description or a more microscopic charges and currents description. The same choice arises at the surface of a polarised dielectric, where there is a E discontinuity.

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