### SUPERCONDUCTIVITY PHYSICS PROBLEMS

The following problems are selected questions dealing with general physics and the physics of the superconductivity. The rationalized mks system of electromagnetic units is used.

1. What is the resistance of a superconductor in the normal state if 300 milliamps of current are passing through the sample and 4.2 millivolts are measured across the voltage probes?
2. What is the resistivity of the rectangular sample in problem #1, if the material is 2.5 mm wide, 3.4 mm high and the distance between the probes is 2.5 cm?
3. Imagine connecting rectangular samples of copper and stainless steel as in problem #3. Typical resistivities of these materials are 1.8 x 10  and 12 x 10   -m, respectively. What resistances will be measured?
4. Consider wiring the superconductor of problems #1 and #2 in series with a 10-ohm resistor and connected to a 1.5-V battery. How much electrical current will flow through the superconductor? What is the critical density required for loss-free current flow?
5. Explain why the electric field inside a superconductor must be equal to zero.
6. A flat superconductor plate levitates magnets by acting as a mirror of magnetic fields. How high will fully magnetized, 1-g blocks of nickel, iron, and neodymium-iron-boron (Nd Fe  B) levitate? Their saturation magnetizations are 0.005, 0.17, and 1.0 A-m /kg, respectively. (These magnetizations give surface magnetic fields of 54, 1700, and 16,000 gauss, respectively.) Note that the repulsive force between two (parallel) magnetic moments of identical values m separated by the distance r is given by F = 3m /r .
7. Electrical current I through a circular wire loop of self inductance L =  b(ln8b/a-7/4) decays over time t according to I = I exp(-tR/L). Two wires of radius a=0.2 mm (0.4-mm thick), length 2 b=19 cm, and resistances, R=10 m and 25  , were wound as circles. Graph the current as a function of time t.

8. The electrical potential around such a loop in the presence of an alternating magnetic field, Bcos( t) is E= b B sin( t). At 60 Hz what are the resulting current flows against the complex electrical impedance, R + i L?
9. The following data was obtained from a YBCO bulk sample. Calculate the resistance for each trial given that a constant current of 100 mA was flowing through the sample.

```
Voltage    T (K)   R (Ohm)   Voltage     T (K)   R (Ohm)

0.0010370   118.2             0.008440    93.5
0.0010270   116.1             0.007830    93.2
0.0010600   114.8             0.006390    93
0.0010490   112.9             0.0005050   92.6
0.0010350   110.9             0.0003790   92.3
0.0010220   109.1             0.0002430   92.1
0.0010090   106.9             0.0000930   91.7
0.0010010   105               0.0000100   91.4
0.0009890   103.5             0.0000030   91
0.0009750   102.2             0.0000002   90.8
0.0009670   100              -0.0000002   90.1
0.0009510    97.9            -0.0000001   89.9
0.0009440    95.8             0.0000003   89.5
0.0009180    95              -0.0000001   88.8
0.0009110    94.3             0.0000001   88.5
0.0008920    93.8
```

10. Using the data from problem #9 make a graph plotting resistance as a function of the temperature.
11. What is the first derivative of the normal, resistive part of the graph?
12. Estimate the critical temperature T from your graph.
13. List and discuss two applications of superconductors that are currently in use today.
14. Discuss the problems that scientists must overcome before superconductors can be used effectively.

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Date posted 04/01/96 (ktb)