  We study the effect caused by external magnetic fields on the observed
thermal spectra and iron line profiles of thin accretion discs formed around
Kerr black holes and naked singularities. We aim to provide a tool that can be
used to estimate the presence of magnetic fields in the neighbourhood of a
compact object and to probe the cosmic censorship conjecture in these
particular astrophysical environments. We developed a numerical scheme able to
calculate thermal spectra of magnetised Page-Thorne accretion discs formed
around rotating black holes and naked singularities as seen by an arbitrary
distant observer. We incorporated two different magnetic field configurations:
uniform and dipolar, using a perturbative scheme in the coupling constant
between matter and magnetic field strength. Under the same assumptions, we
obtained observed synthetic line profiles of the 6.4 keV fluorescent iron line.
We show that an external magnetic field produces potentially observable
modifications on the thermal energy spectrum and the fluorescent iron line
profile. Thermal energy spectra of naked singularities are harder and brighter
than those from black holes, and in addition, peak and cut-off energies are
affected by the external magnetic field. Moreover, iron line profiles of slowly
rotating black holes suffer more changes by a uniform magnetic field, while
nearly extremal black holes and naked singularities are more altered in the
dipolar case. Based on our calculations, we discard the possibility of
modelling the archetypal black-hole candidate in Cygnus X-1 as a naked
singularity. Comparison of our models with observational data can be used to
probe the cosmic censorship conjecture and to estimate the existence and global
geometry of magnetic fields around compact objects by fitting the thermal
energy spectra and iron line profiles of X-ray binaries.
