The transverse magnetic electron scattering form factors of 19O and 21Na exotic nuclei were studied in the plane wave Born approximation (PWBA). The shell model calculations with three sd-shell interactions, USDA, USDB, and Wildenthal, were carried out for the ground and low-lying excited states. The exact center of mass correction in the Born approximation picture through the translation-invariant shell model (TISM) was included to modify the transverse form factors. The measured magnetic dipole moments were well reproduced with the core polarization (CP) effect introduced through the effective g-factors. The occupancies percentage with respect to the valence nucleons was also calculated.