We present a review and discussion of the physical meaning of the vector potential in
electromagnetism by means of a classical experiment in which a long solenoid, connected to
a sinusoidal voltage supply, produces an electric field and a vector potential in a circuit
exterior to the solenoid itself. Some basic considerations are recalled concerning the
meaning of action-at-a-distance and local description, in terms of ‘real fields’ of the induced
electromotive force on the circuit outside the solenoid. From this viewpoint the
roles played by the magnetic field, the electric field and the vector potential to
account for the physical effects are reviewed. Finally, the connections between
these considerations and the magnetic Aharonov–Bohm effect are recalled in the
light of recent theoretical work aimed at explaining the Aharonov–Bohm phase
shift in terms of the magnetic field without resorting to the vector potential.