An uncharged conductor A placed on an insulating stand is brought near a charged insulated conductor B. What happens to the charge and potential of B?

When the uncharged conductor A is brought near a charged insulated conductor B, the charge of B remains the same as they are insulated and the potential of B decreases as it induces charge in conductor A.

Sharply observing, over the surface of charged conductor , there must be influence of charge induced by itself (over other uncharged cond). This way, if I am not wrong, electric field around surface of charged conductor should get altered and consequently charge density must change. Overall there won`t be any effect over net charge but charge density surely should be effected , I guess.