Condition for Nonexistence of Aharonov-Bohm Effect

It is shown that electromagnetic effects of a vector potential on a charged particle confined to a region $R$ (multiply or simply connected) are completely determined by field strengths in $R$, if the potential obeys certain conditions. Such potentials are adequate in experiments purporting to show Aharonov-Bohm effect. Therefore these experiments have not established effects of inaccessible fields.