Conductors are materials that allow free electrons to move freely between atoms and molecules (e.g. metal). In regular conductors the electrons experience resistance to their movement.
Free electrons moving in copper conductor
There are some electrical conductors, called superconductors, where the electrons don't have any resistance to their movement. At present, only materials that are cooled below a certain temperature can have this property. The electrons in these materials group together and magnetic fields are absent.
Paired electrons moving in a superconductor
Watch the Adventures at Nanoscale: Superconductivity video to find out more about superconductivity.
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