6.4 Linear and Nonlinear Media 293 (a) FIGURE 6.31 (b) Problem 6.23 A familiar toy consists of donut-shaped permanent magnets (magne- tization parallel to the axis), which slide frictionlessly on a vertical rod (Fig. 6.31). Treat the magnets as dipoles, with mass ma and dipole moment m. (a) If you put two back-to-back magnets on the rod, the upper one will "float"—the magnetic force upward balancing the gravitational force downward. At what height (z) does it float? (b) If you now add a third magnet (parallel to the bottom one), what is the ratio of the two heights? (Determine the actual number, to three significant digits.) [Answer: (a) [3µom²/2лmɑg] ¹⁄4; (b) 0.8501] Problem 6.24 Imagine two charged magnetic dipoles (charge q, dipole moment m), constrained to move on the z axis (same as Problem 6.23(a), but without gravity). Electrically they repel, but magnetically (if both m's point in the z direction) they attract. (a) Find the equilibrium separation distance. (b) What is the equilibrium separation for two electrons in this orientation. [Answer: 4.72 x 10-13 m.] (c) Does there exist, then, a stable bound state of two electrons?

6.4 Linear and Nonlinear Media 293 (a) FIGURE 6.31 (b) Problem 6.23 A familiar toy consists of donut-shaped permanent magnets (magne- tization parallel to the axis), which slide frictionlessly on a vertical rod (Fig. 6.31). Treat the magnets as dipoles, with mass ma and dipole moment m. (a) If you put two back-to-back magnets on the rod, the upper one will "float"—the magnetic force upward balancing the gravitational force downward. At what height (z) does it float? (b) If you now add a third magnet (parallel to the bottom one), what is the ratio of the two heights? (Determine the actual number, to three significant digits.) [Answer: (a) [3µom²/2лmɑg] ¹⁄4; (b) 0.8501] Problem 6.24 Imagine two charged magnetic dipoles (charge q, dipole moment m), constrained to move on the z axis (same as Problem 6.23(a), but without gravity). Electrically they repel, but magnetically (if both m's point in the z direction) they attract. (a) Find the equilibrium separation distance. (b) What is the equilibrium separation for two electrons in this orientation. [Answer: 4.72 x 10-13 m.] (c) Does there exist, then, a stable bound state of two electrons?

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter29: Magnetic Fields

Section: Chapter Questions

Problem 29.1CQ: Can a constant magnetic field set into motion an electron initially at test? Explain your answer.

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