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InterviewSolution
| 1. |
Demonstarate that electronsmove in a betatronalong around orbitof constantradiusprovidedthe magnetic induction on the orbitof constantradiusprovidedthe magnetic inductionon the orbitis equalto halfthe meanvalue of that indide the orbit (the betatron condition). |
| Answer» <html><body><p></p>Solution :On the one hand, <br/> `(dp)/(dt) = eE = (e)/(2pi r) (d Phi)/(dt) = (e)/(2pi r) (d)/(dt) int_(0)^(r) 2pi r' <a href="https://interviewquestions.tuteehub.com/tag/b-387190" style="font-weight:bold;" target="_blank" title="Click to know more about B">B</a> (r') dr'` <br/> On the other, <br/> `p = B (r) er, r` = constant. <br/> so, `(dp)/(dt) = er (d)/(dt) B(r) = er dotB (r)` <br/> Hence, `er dotB (r) = (e)/(2 pi r) pi r^(2) (d)/(dt) <a href="https://interviewquestions.tuteehub.com/tag/lt-537906" style="font-weight:bold;" target="_blank" title="Click to know more about LT">LT</a> B gt` <br/>So, `dotB (r) = (<a href="https://interviewquestions.tuteehub.com/tag/1-256655" style="font-weight:bold;" target="_blank" title="Click to know more about 1">1</a>)/(2) (d)/(dt) lt B gt` <br/> This is most <a href="https://interviewquestions.tuteehub.com/tag/easily-964537" style="font-weight:bold;" target="_blank" title="Click to know more about EASILY">EASILY</a> <a href="https://interviewquestions.tuteehub.com/tag/satisfied-636887" style="font-weight:bold;" target="_blank" title="Click to know more about SATISFIED">SATISFIED</a> by taking`B(r_(0)) = (1)/(2) lt B gt` .</body></html> | |