The self-assembly of many viral capsids is dominated by protein protein electrostatic interactions. To have a better understanding of this process, it is important to know how the protein and the capsid surface charges vary as a function of the pH and ionic strength. In this work, using phase analysis light scattering, we measured the electrophoretic mobility (EM) of the cowpea chlorotic mottle virus (CCMV), its capsid protein (CP), and a cleaved CP that lacks its basic terminus, as a function of pH and ionic strength. The EM measurements of the CP are difficult to carry out due to its tendency to self-assemble into capsids; we show how to circumvent this problem by appropriately changing the CP concentration. We found that the isoelectric points (pIs) of the virion and of the CP are insensitive to ionic strength. The onset of multishell structures in the phase diagram of the CCMV CP as a function of ionic strength and pH (and its absence in the brome mosaic virus (BMV) CP phase diagram) can be related to the pI of the capsid. We propose that the transition from multiwall shells to nanotube structures is due to a change in the spontaneous curvature of the CP at its pI. A nonzero limit of the EM at high ionic strength is characteristic of a soft colloid, but a near identity of the EMs of empty capsids and those containing RNA indicates that the EM reflects only the charge distribution in the CP. The Henry equation has been used to provide approximate values of the capsid surface charge as a function of pH and I.