# Worksheet: Superconductors

In this worksheet, we will practice calculating the properties required for a superconductor to operate, referring to its critical temperature and critical field.

Q1:

At what temperature, in terms of the critical temperature , is the critical field of a superconductor one-half its value at ?

• A
• B
• C
• D
• E

Q2:

A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50-Ω resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed? The critical temperature of Pb is 7.2 K and the critical field value for Pb is 0.080 T.

Q3:

Measurements of a superconductor’s critical magnetic field at various temperatures are shown in the accompanying table. Determine the value of the critical magnetic field at absolute zero. Assume a critical temperature value of 7.2 K.

 𝑇 (K) 𝐵 (T) 3 3.5 4.5 6 6.5 0.066 0.061 0.049 0.024 0.015

Q4:

A tightly wound solenoid at a temperature of 4.2 K is 60 cm long and is constructed from a Pb wire of radius 1.6 mm. Find the maximum current that the solenoid can carry at which the wire remains superconducting. Use a value of 7.2 K for the critical temperature and use a value of 0.080 T for the value of the critical magnetic field at absolute zero.

Q5:

Find the critical magnetic field of Mercury at 2.6 K. Use a value of 4.2 K for the critical temperature and use a value of 0.041 T for the value of the critical magnetic field at absolute zero.