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The goal of our study is to detect and characterize the electromagnetic waves that can modify the electron distribution functions, with a special attention to whistler waves. We analyse in details the electric and magnetic field fluctuations observed by the Solar Orbiter spacecraft during its first orbit around the Sun between 0.5 and 1 AU. Using data of the Search Coil Magnetometer and electric antenna, both parts of the Radio and Plasma Waves (RPW) instrumental suite, we detect the electromagnetic waves with frequencies above 3 Hz and determine the statistical distribution of their amplitudes, frequencies, polarization and k-vector as a function of distance. We also discuss relevant instrumental issues regarding the phase between the electric and magnetic measurements and the effective length of the electric antenna. An overwhelming majority of the observed waves are right hand circularly polarized in the solar wind frame and identified as outward propagating and quasi parallel whistler waves. Their occurrence rate increases by a least a factor two from 1 AU to 0.5 AU. These results are consistent with the regulation of the heat flux by the whistler heat flux instability. Near 0.5 AU, whistler waves are found to be more field-aligned and to have smaller normalized frequency ($f/f_{ce}$), larger amplitude, and larger bandwidth than at 1 AU., Comment: accepted in A&A