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.

- 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?
- 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?
- 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?
- 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?
- Explain why the electric field inside a superconductor must be equal to zero.
- 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 (NdFeB) 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*= 3*m**/r*. - 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*. - The electrical potential around such a loop in the presence of an
alternating magnetic field,
*B*cos(*t*) is*E*=*b**B*sin(*t*). At 60 Hz what are the resulting current flows against the complex electrical impedance,*R + iL*? - 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 - Using the data from problem #9 make a graph plotting resistance as a function of the temperature.
- What is the first derivative of the normal, resistive part of the graph?
- Estimate the critical temperature
*T*from your graph. - List and discuss two applications of superconductors that are currently in use today.
- Discuss the problems that scientists must overcome before superconductors can be used effectively.

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