The deep I Hα line core and a typical observed V/I circular polarisation spectrum of 40 Eri B is compared to similar line cores and polarisation spectra of two magnetic Ap stars, HD 16605 and HD 49299, all observed with ESPaDOnS. The two magnetic Ap stars both have magnetic fields of ⟨ B_z ⟩ ~ 2.5 kG at the time of observation. The V/I spectrum of 40 Eri B shows no sign of a magnetic signature at a level several times smaller than the signals clearly visible in the V/I spectra of the Ap stars. All I spectra are normalised to 1.0 in the continuum, shifted vertically by +0.3 (HD 42999) or +0.6 (HD 16605); V/I spectra are shifted downward from 0.0 by –0.2 (HD 49299) or –0.4 (40 Eri B).