Final answer:
In an ideal superconductor with no applied potential difference, the current would be zero because there's no electric field to drive the current. Superconductors have zero electrical resistance and can maintain a current indefinitely once established. Practical applications of superconductors are challenged by their need for extremely low temperatures.
Step-by-step explanation:
If an ideal superconductor is left alone with no potential difference applied, the current flowing in it would be zero. This assertion may seem paradoxical when considering Ohm's Law (V=IR), which suggests that with R=0, any finite voltage would lead to infinite current. However, in the absence of a voltage source, there's no electric field to drive a current, and therefore no current will initiate.
It's important to note that superconductors exhibit a property of zero electrical resistance, which means there are no heat losses for currents passing through them, making them perfect for applications requiring high currents with no energy losses, like in MRI machines or power transmission. Yet, the intriguing feature of superconductors is that once a current is established within them, it can persist without decaying for a very long time, potentially indefinitely, because there are no resistive losses to dampen the flow of electrons.
Overall, the nature of superconductivity allows for many practical applications due to these unique properties. The challenge with superconductors remains in maintaining the very low temperatures needed for them to exhibit zero resistivity, although recent advances have been made in developing high-temperature superconductors.