Superconductivity and the Meissner effect

What just happened?

Above the critical temperature the sample is an ordinary metal — its resistance rises linearly with temperature. Once cooled below $T_c$ the resistance drops abruptly to zero: the material enters the superconducting state.

Resistance vs. temperature:

— for a metal the resistance is directly proportional to temperature, but at the critical temperature $T_c$ a sudden jump appears: $R = 0$. For YBCO $T_c \approx 92\,\mathrm{K}$.

Current without losses:

When $R = 0$, current flows through the sample, but no Joule heat is released:

Charges flow without resistance — once started, a current can circulate in a superconducting loop practically forever.

Meissner effect:

Below $T_c$ the superconductor expels the magnetic field from its interior ($B = 0$ inside). Screening currents on the surface create a field opposing the external one — that is why the magnet rises and levitates above the sample. Maglev trains exploit this phenomenon.

Where does this work?

Superconductors carry enormous currents without losses — hence the strong electromagnets in MRI scanners, particle accelerators, and levitating maglev trains.

Why this matters for the exam:

This extends the topic of electrical resistance and its dependence on temperature and magnetic field. Trick: check whether $T$ is above or below $T_c$ — that decides whether the resistance rises with temperature or is exactly zero (and then $P = I^2R = 0$).

Remember: below the critical temperature a superconductor's resistance is exactly zero — the current flows without losses, and the magnetic field is expelled (Meissner effect → levitation).