In a dielectric‐loaded waveguide a slow rotating equilibrium of a relativistic electron beam which interacts with the electromagnetic waves is investigated in a self‐consistent way. General dispersion relations for the fundamental transverse magnetic modes in the presence of the external magnetic field are derived using the cold fluid Maxwell equations and the appropriate boundary conditions. For slow space charge and slow cyclotron modes an algebraic equation is obtained from the dispersion relation by using a tenuous beam approximation. Solutions of the resulting equation are obtained for variations of several parameters, such as the external magnetic field, the dielectric constant, the thickness of the dielectric material, and the gap between beam and dielectric materials. With the beam‐dielectric gap satisfying the stability condition, the growth rate of the space charge and the slow cyclotron instabilities show the same behavior as previous results for the no gap case [IEEE Trans. Plasma Sci.PS‐17576 (1989)]. Finally, emphasis in the analysis is given to the effect of the finite gap between the beam and dielectric and the comparison to the previous study of a no‐gap case. From this analysis it is also shown that as the gap width increases, the growth rate, &ohgr;icdecreases due to the finite geometric effect related to the gap width.