= Demagnetizing field
{title2=$\mathbf H_d$}
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The <demagnetizing field> is the contribution to <magnetic field intensity> produced by the sample's own <magnetization>. Inside a uniformly magnetized <ellipsoid>, it is uniform and has the form $\mathbf H_d=-\mathsf N\mathbf M$; the <demagnetizing factor> along a principal axis gives its longitudinal component. These conditions make the scalar correction in <field conventions for magnetic susceptibility> useful.
A cylinder generally has spatially varying <magnetization> and <demagnetizing field>. A volume-sensitive instrument and a short central pickup coil consequently need different effective corrections: one averages over the sample, while the other samples central flux. A shape factor copied from an <ellipsoid> is not an exact correction for every cylinder, especially with nonlinear response or <hysteresis>. <Concise Encyclopedia of Magnetic & Superconducting Materials/Demagnetizing Factors>[R. B. Goldfarb, Demagnetizing Factors, printed p. 104, §2 opening paragraphs: magnetometric versus fluxmetric sensing, nonuniform cylindrical fields and susceptibility-dependent factors]{ref}
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