An essential part of experimental program at the future Electron Ion Collider is the study of the nuclear structure and dynamics at low x. DIS at low x is characterized by large longitudinal coherence length that by far exceeds radii of heavy nuclei. The coherent behavior is essential feature of the nuclear matter at low x. This pertains not only to the strong interactions, but also to electromagnetic ones. Coherent interactions of a projectile with nucleons in a heavy nucleus are characterized by parameters α 2 s A 1/3 ∼ 1 and αZ ∼ 1 in strong and electromagnetic interactions respectively. Contributions exhibiting non-trivial dependence on αZ are called the Coulomb corrections. We compute the Coulomb corrections to the cross sections of the semi-inclusive and diffractive DIS. We show that they violate the geometric scaling in a wide range of photon virtualities and is weakly x-independent. In heavy nuclei at low Q 2 the Coulomb correction to the total and diffractive cross sections is about 20% and 40% correspondingly