[Physics] Is potential difference always required for current


Say we use a cell to give rise to a current in a circuit and then remove the cell such that the circuit doesn't break. It means that no potential difference exists between any two points in the circuit since a circuit wire with current is neutral. So will the circuit wire have a decreasing current after I remove the battery due to N1L and Galileos definition of inertia that a body's state of rest or motion cannot be changed without an external force acting on it? Also does this mean that a superconductor will have constant current flowing through it even after removing the voltage source since there is no resistance to slow it down?

Best Answer

Persistent currents
Persistent currents is the name given to the currents flowing without energy dissipation and therefore not requiring a voltage bias to be sustained. This is notably the currents in superconductors (already mentioned in the answer by @kruemi), but also currents in some mesoscopic devices, where the energy cannot be dissipated due to the size effects (e. g., lack of efficient coupling to phonon bath and/or restrictions on the electron momentum change). Note however that the currents on microscale generally do not follow the same rules as those for conventional circuits - in particular, the lumped-circuit description fails (see also my answer to Are voltages discrete when we zoom in enough?).

Diffusion currents, etc.
As less exotic options one could mention diffusion current, where the current is due to the difference in electron concentrations, rather than bias. This is however difficult to sustain for a long time, and it usually co-exist with conventional (drift) current, as, e.g., in pn junctions.

Thermoelectric and other phenomena
Onsager relations predict a number of phenomena where the current can arise from spatial variation in other thermodynamic parameters. The diffusion current above can be viewed as the result of a gradient in chemical potential. Another well-known case is thermoelectric phenomena. These are often expressed in terms of voltage at the terminals of a device, due to the accumulated charge, but in a bulk they are actually currents.