How much work is required to move a 1 coulomb charge a distance of 2 meters along an equipotential line or conductor of 12.5 volts

Work done to move a charge is

(quantity of charge) x (potential difference during the move).

Notice that the distance doesn't matter ... only the volts of

potential change along the way.

If the route is along an equipotential line, there is no potential

difference, so it doesn't take any work.

Through a conductor, it also doesn't take any work, if the whole

conductor is at the same potential.

That never happens in a real conductor, like a copper wire or a

cable at normal temperature. There's always some potential

difference along the conductor, so it takes some work to move it

through.

BUT ... strange as it may seem ... the so-called 'superconductors',

which are exotic materials at ridiculously low temperatures, have

literally NO resistance. Not just very low, but zero! If you start

a current flowing in a superconductor material, and then submerge

it in liquid helium at a few degrees above absolute zero, you can

disconnect the battery and connect the ends of the superconductor

together, and as long as you keep it cold, the current continues to

flow around and around in the superconductor, with no loss, for

months or longer! It sure sounds weird, but this is how they build

the super-strong electromagnets in CT and MRI machines. ((I guess

that's why it costs so much to get a set of 8-by-10 color glossies from

your CT scan. They don't snap 'em with their smartphone.)