The Meissner effect Compare this problem with Problem 65 in Chapter 26, on the force attracting a perfect dielectric into a strong electric field. A fundamental property of a Type I superconducting material is perfect diamagnetism, or demonstration of the Meissner effect, illustrated in Figure 30.35, and described as follows. The superconducting material has B = 0 everywhere inside it. If a sample of the material is placed into an externally produced magnetic field, or if it is cooled to become superconducting while it is in a magnetic field, electric currents appear on the surface of the sample. The currents have precisely the strength and orientation required to make the total magnetic field zero throughout the interior of the sample. The following problem will help you to understand the magnetic force that can then act on the superconducting sample. A vertical solenoid with a length of 120 cm and a diameter of 2.50 cm consists of 1 400 turns of copper wire carrying a counterclockwise current of 2.00 A, as in Figure P32.79a.
(a) Find the magnetic field in the vacuum inside the solenoid.
(b) Find the energy density of the magnetic field, and note that the units J/m3 of energy density are the same as the units N/m2 of pressure.
(c) Now a superconducting bar 2.20 cm in diameter is inserted partway into the solenoid. Its upper end is far outside the solenoid, where the magnetic field is negligible. The lower end of the bar is deep inside the solenoid. Identify the direction required for the current on the curved surface of the bar, so that the total magnetic field is zero within the bar. The field created by the super currents is sketched in Figure P32.79b, and the total field is sketched in Figure P32.79c.
(d) The field of the solenoid exerts a force on the current in the superconductor. Identify the direction of the force on the bar.
(e) Calculate the magnitude of the force by multiplying the energy density of the solenoid field times the area of the bottom end of the superconducting bar.

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