Suppose I have the following circuit with lamp connected and there's also a really long neutral ( total charge zero ) conducting wire under the circuit as follows :
Then , from the theory of electromagnetism, it is known that the potential at distance $ r $ from the conducting neutral wire ( colored in black ) is: $ V(r) \propto \lambda ln(r_0/r) $ where $r_0$ is some reference radius and $ \lambda $ is the charge density of the wire.
So, since there exists a potential from the wire, then the circuit will 'feel it' and charge will flow in the circuit for a brief period of time as shown in the picture below:
The charge flows this way because the potential is higher when we get closer to the conducting neutral wire ( colored in black in the previous image ) and is lower when we get further away from the wire ( so charge flows from higher potential to lower potential ), in addition, charge carriers in the circuit loop rearrange themselves, in such a way that the field inside the conducting loop is zero. This happens for extremely short time.
So there exists a charge flow in the circuit, but such charge flow won't turn the lamp on because the total current in the circuit will be zero ( since the superposition of two currents with equal magnitude but different directions will give zero ) ...
Ok then, in this specific example the total current in the circuit is zero...
But what if there was a different neutral object ( not neccesarily a wire ) creating a potential field such that the total current in the circuit is not zero? could such situation even exist? if it does, then how come electric stuff dont just get turned on randomly at real life ( we wouldn't need batteries and etc )? is it perhaps because the current\potential produced is too low?