Context. The Ap stars that rotate extremely slowly, with periods of decades to centuries, represent one of the keys to the understanding of the processes leading to the differentiation of stellar rotation. Aims. We characterise the variations of the magnetic field of the Ap star HD 50169 and derive constraints about its structure. Methods. We combine published measurements of the mean longitudinal field <Bz> of HD 50169 with new determinations of this field moment from circular spectropolarimetry obtained at the 6-m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. For the mean magnetic field modulus <B>, literature data are complemented by the analysis of ESO spectra, both newly acquired and from the archive. Radial velocities are also obtained from these spectra. Results. We present the first determination of the rotation period of HD 50169, Prot = (29.04+/-0.82) y. HD 50169 is currently the longest-period Ap star for which magnetic field measurements have been obtained over more than a full cycle. The variation curves of both <Bz> and <B> have a significant degree of anharmonicity, and there is a definite phase shift between their respective extrema. We confirm that HD 50169 is a wide spectroscopic binary, refine its orbital elements, and suggest that the secondary is probably a dwarf star of spectral type M. Conclusions. The shapes and mutual phase shifts of the derived magnetic variation curves unquestionably indicate that the magnetic field of HD 50169 is not symmetric about an axis passing through its centre. Overall, HD 50169 appears similar to the bulk of the long-period Ap stars.
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