= Solution
As $B$ changes, each quantized orbit area grows linearly with field while the <Fermi surface> cross-section stays approximately fixed. Landau energies repeatedly cross the <Fermi energy>, making the <density of states> there oscillate. If the relevant extremal orbit has area $S_F$, its crossings satisfy
$$
\frac1{B_n}=\frac{2\pi e}{\hbar S_F}\left(n+\frac12\right),\qquad
\boxed{\Delta(1/B)=\frac{2\pi e}{\hbar S_F}.}
$$
Thus the oscillations are periodic in inverse field rather than field. In three dimensions integration over longitudinal momentum makes extremal cross-sections dominate.
One observable is the <de Haas-van Alphen effect>: the field-dependent occupation changes the electronic free energy, so its field derivative, the <magnetization>, oscillates. The corresponding oscillations of longitudinal <electrical resistance> are the <Shubnikov-de Haas effect>. Both probe Fermi-surface geometry.
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