= Persistent current in a superconducting loop experiment
The <persistent current in a superconducting loop experiment> prepares a closed cold path, changes the externally linked <magnetic flux>, and follows the resulting <superconducting persistent current> through its <magnetic field>. The essential measurement starts after the inducing <magnetic field> has stopped changing.
\Image[/persistent-superconducting-current-geometry.png]
{title=Preparing a closed superconducting loop and sensing its magnetic field with a compass}
{description=Original schematic of field preparation and magnetic compensation. Shapes, winding counts and distances are illustrative. The <magnetic compass> senses a static <magnetic field>; it is not a stationary voltage-reading <pickup coil>.}
<Heike Kamerlingh Onnes>'s 1914 Communication 140c describes a <lead> coil closed by fused <lead> connections. Cooling in a <magnetic field> and removing the inducing magnet prepared the circulation. A <magnetic compass> sensed it without contacts; a separate <copper> coil, cooled in liquid air, supplied a measured balancing <magnetic field>. Reversing orientation and compensation reduced offsets. <Further Experiments with Liquid Helium, J (Continued) by Heike Kamerlingh Onnes>[Communication 140c (1914), §5, pp. 278–280; §7, pp. 280–281]{ref}
The liquid-<helium> <cryostat> maintained low <temperature>, but refilling temporarily warmed the apparatus and changed the inferred <electric current>. A later run used a smaller initial <electric current>. Apparatus deformation and needle-zero drift limited comparison; cutting the closure still left a smaller magnetic signal, warning against assigning every signal to circulation around the whole loop. The report consequently gave an upper bound under a residual <Ohm's law> hypothesis. <Further Experiments with Liquid Helium, J (Continued) by Heike Kamerlingh Onnes>[Communication 140c, §5, pp. 279–280; §6, p. 280; §8, pp. 281–283]{ref}
For interpreting such a measurement, write a locally calibrated magnetic signal as
$$
S(t)=k(t)I(t)+b(t).
$$
Here $k$ is the coupling and gain, while $b$ contains the background <magnetic field> and readout offset. Only after establishing stable $k$ and correcting $b$ does a ratio of signals determine a ratio of <electric currents>. A gradual change in geometry, a drifting background <magnetic field>, or a change of <temperature> can imitate or conceal a decay. A <pickup coil> connected only to a voltage meter obeys <Faraday's law of induction> and detects a changing linked <magnetic flux>; its zero steady output cannot demonstrate that the underlying static <magnetic field> has disappeared. A <magnetic compass> can respond to that static <magnetic field>.
Opening the path, reversing the preparation, and repeating with smaller initial <electric current> are useful controls for separating whole-loop circulation, magnetic background and a <superconducting critical current>. Keep the <temperature> and external <magnetic field> stable during the interval used to infer <electrical resistance>. A sudden reduction near a <superconducting critical current> is not evidence for the constant-$R$ <exponential decay> model at smaller <electric current>. Persistence also does not replace the <Field-cooled Meissner experiment>: transport around a hole and magnetic expulsion from the material test different properties.
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