In the inflation theory with a dilatonic coupling between the inflaton and the U(1) gauge field, a persistent electric field (and then an anisotropic inflation) is obtained as a solution of the classical field equations. We studied the pair production of charged scalar particles in the inflaton-driven electric field. In particular, we evaluated the induced current due to the pair production. Solving the field equations with the induced current, we showed that the first-order backreaction screens the electric field with the cosmic expansion. This result indicates that the no-go theorem of anisotropic inflations holds true regardless of whether the dilatonic coupling is present or not. If time allows, we also comment on future directions of this topic, i.e. i) induced current on general backgrounds, ii) pair productions of charged fermions. This talk is based on Phys. Rev. D98 (2018) 103512 and work in progress.