Introduction to Electrodynamics · Problem 7.52

Conservation Laws — David J. Griffiths

Physics · diamagnetism-orbit-radius

Problem

An atomic electron (charge qq) circles about the nucleus (charge QQ) in an orbit of radius rr; the centripetal acceleration is provided, of course, by the Coulomb attraction of opposite charges. Now a small magnetic field dBdB is slowly turned on, perpendicular to the plane of the orbit. Show that the increase in kinetic energy, dTdT, imparted by the induced electric field, is just right to sustain circular motion at the same radius rr. (That's why, in my discussion of diamagnetism, I assumed the radius is fixed. See Sect. 6.1.3 and the references cited there.)

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