I need clarification as to whether persistent currents can last for 1,023 years or 10 to the 23rd power (indefinitely). There’s a huge difference in magnitude between these two figures.
The practical reality is far from the theoretical absolute
Read the link and the goodle book for the full story. YA will not let me post it all.
Persistent Current Demonstration
What happens when you remove the toroid from the liquid nitrogen bath and repeat an attempt to deflect the compass needle?
Is one application of this effect a powerful permanent magnet? If so, what are its advantages and limitations over existing permanent magnets?
If you repeat this experiment but do not use a magnet to induce an electrical current in the toroid, what are the compass needle deflection results that you would expect to see?
Could you use this phenomena to estimate the Critical Temperature? If so, how?
Can you design a system for withdrawing the electrical energy out of our storage ring toroid for use?
What are some other potential applications of the persistent electrical current in a toroidal coil?
The amount of deflection of the compass needle can be used to obtain a rough measurement of the current that has been induced in the toroid. The provided scale with compass will allow one to obtain the value of the deflection. The deflection will have to be corrected for the Meissner Effect by successively measuring the deflection for either the two different poles of the compass needle, or the deflection caused by the two faces of the toroid for the same pole of the compass needle. Please see figure 9 below for the positioning of the experimental components. Figure 10 shows the different variables and the configuration of the compass needle and toroid.
Estimation of the value of the induced current
The induced superconducting current represents a stored electric current, and can be shown to persist for extremely long periods of time as long as the toroidal ring is kept at liquid nitrogen temperatures. If this experiment were to be scaled up in size, the stored electrical energy could potentially be used at any later time. This is the principle of the U.S. Navy’s SMES experiment.
This semi-quantitative measurement of the persistent current in the toroid requires an estimation of the deflection of the needle (shown as the angle ø in figure 10 above), and the distance of the needle tip from the center of the toroid (distance x in figure 10). The deflection of the compass needle at distance ‘x’ from the toroid, is the result of a combination of forces exerted by the horizontal component of earth’s magnetic field (ßearth) and the magnetic field due to the toroid (ßtoroid). The relation between these quantities is simply:
ßtoroid = ßearth tanø
The horizontal component of the earth’s magnetic field is about 2 X 10-4 Tesla (2 Gauss). This value varies slightly with one’s position on the earth. From this estimation of the magnetic field of the toroid, the Biot-Savart Law or Ampere’s can be used to calculate the current induced (Itoroid) and extant in the toroid.
Itoroid = (2ßtoroid(x2 + r2)3/2)/µr2
Here ‘r’ is the average radius of the toroid and is approximately 0.0095 meters (see figure 10), and µ is the permeability of free space and is equal to (4*pi) X 10-7 Newton/Amp2.
r = raverage = (Outer diameter + Inner diameter)/4
All units in this form of the Biot-Savart Law are SI (Standard International) units. Distances x and r are in meters, magnetic field strength ß is in Tesla, and Current I is in Amperes.
The amount of current in the toroid (Itoroid), can be increased by increasing the strength of the magnet used to induce the current. However, the magnet that has been provided is already one of the most powerful commercially available magnets. Several passes in the same direction with a magnet should also work. Use of an electromagnet for inducing the current in the toroid may offer the best solution.
Instead of using a compass to determine the magnetic field of the toroid, a Hall-probe Gaussmeter can be used for a much more accurate measurement. This approach has the added advantage that the toroidal ring superconductor can remain in a horizontal position throughout the experiment.
Estimation of the lifetime of the persistent current.
The existence of a persistent current in the toroidal ring has already been amply demonstrated by our compass needle deflection experiment. However, it would be instructive to actually attempt to measure the decay of the electrical current as a function of time.
The initial expectation is that there should simply be no decay of the persistent electrical current over time since, after all, the toroid is a superconductor, and exhibits no electrical resistance, and hence no energy loss. Practically however, on account of the phenomena of flux creep and flux flow one will see a very small exponential decay of the stored electrical current. It would be very instructive to investigate this decay because it provide an insight into the effective `resistance’ of the superconducting toroid.
The simplest approach is to first induce an electrical current in the toroid as per the procedure described above. It is however recommended that you should use a Gaussmeter for this experiment on account of the precise measurements that are required. The toroid with its induced persistent current will then have to be stored at liquid nitrogen temperatures over a period of several weeks. The current in the toroid is measured at periodic intervals over this time. Care will need to be exercised to prevent heating any portion of the toroid during the duration of the investigation.
If the results of measurement of the electrical current in the toroid were plotted versus the time intervals over which these measurements were made, it will be seen that the current decays exponentially as a function of time as described the following relationship:
e-(R/L)t = F
Where R is the electrical resistance of the toroid, L is the inductance of the toroid, and F is the fraction of the remaining electrical current at time t. Our own measurements indicate that for the toroidal ring in the Superconducting Energy Storage Kit, the value of L is about 5 nH (nano Henry). Using this number we have obtained a value of the toroid ring electrical resistance equal to 10-15 ohms.
Working backwards, using the measured value of R above, the time required for the current to decrease to 50% of its original value, we find that:
tI=0.5 = 1023 years
Note: This is an approximate value.
This indicates that for most practical purposes, the current is permanently stored in the toroidal ring superconductor.
on: 23rd September 07