8 Two moving charged particles exert forces on each other because each creates a magnetic field that acts on the other. These two "Lorentz" forces are proportional to vix (2 xr) and 2 x (vi x-r), where is the vector between the particle positions. Show that these two forces are equal and opposite in accordance with Newton's third law if and only if rx (vi × 2) = 0.
8 Two moving charged particles exert forces on each other because each creates a magnetic field that acts on the other. These two "Lorentz" forces are proportional to vix (2 xr) and 2 x (vi x-r), where is the vector between the particle positions. Show that these two forces are equal and opposite in accordance with Newton's third law if and only if rx (vi × 2) = 0.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter14: Special Theory Of Relativity
Section: Chapter Questions
Problem 14.21P
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Transcribed Image Text:8
Two moving charged particles exert forces on each other because each creates a magnetic field that acts
on the other. These two "Lorentz" forces are proportional to vix (2 xr) and 2 x (vi x-r), where is the vector
between the particle positions. Show that these two forces are equal and opposite in accordance with Newton's third
law if and only if rx (vi × 2) = 0.
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