Debye series expansion (DSE) is developed for electromagnetic (light) scattering by a charged sphere. By comparing our results with Mie theory (for a charged sphere) and with DSE (for a neutral sphere), we verify our theory numerically. DSE is employed for calculation of far-field intensity, and absorption and extinction efficiencies of charged spherical particles illuminated by a plane wave. The influences of various parameters (including surface charge, refractive index, size parameters, Debye mode, etc.) are studied. The rainbow produced by charged particles is analyzed. These results are of great significance in many fields including particle sizing, optical tweezers, etc.