system
Given the following post, respond as if you're commenting on Reddit:
human
For a superconductor of a certain size, is there a limit to how much current can run through it?

My thoughts are that with normal(copper, aluminum) conductors, the main current limits come from resistance in the conductor causing the conductor to heat up when too much current is passed through it.  If the conductor had no resistance, however, what would that limit be, if there was one?
gpt
The problem with trying to pass huge amounts of current through a superconductor is that any flowing current creates a magnetic field circling around it (Ampere's law). A superconductor also expels all magnetic fields from inside itself (Meissner effect), so what you get is a lot of magnetic field lines all bunched up just outside the surface of the superconductor, which makes a strong magnetic field there.

Magnetic fields kill superconductivity. Every superconductor has a "critical field" at which it stops superconducting (which actually depends strongly on temperature). So at some point the magnetic field produced by the current will be too much for the superconductor to handle, and it will "quench", which means it abruptly stops superconducting, and then the energy in the flowing current is very rapidly turned into heat.