The dynamics of electron beams from magnetically shielded guns is examined in detail both experimentally and theoretically. The electron orbits and beam shape variations are investigated with an electron beam analyzer which measures current density variations and transverse velocity. The existence of rings of charge that move through the beam and the gradual reduction in beam scalloping with length are demonstrated. It is shown that simple energy considerations plus an account of the role of transverse thermal velocities is sufficient to account for the experimentally observed features of beam behavior in the limit of negligible space charge. In the presence of space charge the beam behavior is qualitatively unchanged except for some defocusing and precession of the electron orbits provided that the magnetic field is at least several times the Brillouin field.