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An atomic electron (charge q) circles about the nucleus
Chapter 7, Problem 52P(choose chapter or problem)
Problem 52P
An atomic electron (charge q) circles about the nucleus (charge Q) in an orbit of radius r ; the centripetal acceleration is provided, of course, by the Coulomb attraction of opposite charges. Now a small magnetic field dB is slowly turned on, perpendicular to the plane of the orbit. Show that the increase in kinetic energy, dT, imparted by the induced electric field, is just right to sustain circular motion at the same radius r. (That’s why, in my discussion of diamagnetism, I assumed the radius is fixed. See Sect. 6.1.3 and the references cited there.)
Questions & Answers
QUESTION:
Problem 52P
An atomic electron (charge q) circles about the nucleus (charge Q) in an orbit of radius r ; the centripetal acceleration is provided, of course, by the Coulomb attraction of opposite charges. Now a small magnetic field dB is slowly turned on, perpendicular to the plane of the orbit. Show that the increase in kinetic energy, dT, imparted by the induced electric field, is just right to sustain circular motion at the same radius r. (That’s why, in my discussion of diamagnetism, I assumed the radius is fixed. See Sect. 6.1.3 and the references cited there.)
ANSWER:
Solution
Step 1 of 3
In this problem, we have to show that there is an increase in kinetic energy. The centripetal force of an object of mass m in circular path is given by .
Where v is the velocity and r is the radius.