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If a negative charge q (an electron, for example) in an
Chapter 9, Problem 9.22(choose chapter or problem)
If a negative charge q (an electron, for example) in an elliptical orbit around a fixed positive charge Q is subjected to a weak uniform magnetic field B, the effect of B is to make the ellipse precess slowly an effect known as Larmor precession. To prove this, write down the equation of motion of the negative charge in the field of Q and B. Now rewrite it for a frame rotating with angular velocity Si [Remember that this changes both d2r/dt2 and drldt.] Show that by suitable choice of St you can arrange that the terms involvingr cancel out, but that you are left with one term involving B x (B x r). If B is weak enough this term can certainly be neglected. Show that in this case the orbit in the rotating frame is an ellipse (or hyperbola). Describe the appearance of the ellipse as seen in the original nonrotating frame.
Questions & Answers
QUESTION:
If a negative charge q (an electron, for example) in an elliptical orbit around a fixed positive charge Q is subjected to a weak uniform magnetic field B, the effect of B is to make the ellipse precess slowly an effect known as Larmor precession. To prove this, write down the equation of motion of the negative charge in the field of Q and B. Now rewrite it for a frame rotating with angular velocity Si [Remember that this changes both d2r/dt2 and drldt.] Show that by suitable choice of St you can arrange that the terms involvingr cancel out, but that you are left with one term involving B x (B x r). If B is weak enough this term can certainly be neglected. Show that in this case the orbit in the rotating frame is an ellipse (or hyperbola). Describe the appearance of the ellipse as seen in the original nonrotating frame.
ANSWER:Step 1 of 3
The equation of motion for this particle is 