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GR9677 #86
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Problem
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This problem is still being typed. |
Electromagnetism }Particle Trajectory
There is a force pointing upwards from the Electric field in the y-direction. Suppose the particle is initially moving upwards. Then, the magnetic field would deflect it towards the right... One can apply the Lorentz Force to solve this problem.
If the particle comes in from the left, then the magnetic force would initially deflect it downwards, while the electric force would always force it upwards. Continue applying this analysis to each diagram. It turns out that one has cycloid motion whenever the electric and magnetic fields are perpendicular.
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Alternate Solutions |
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Comments |
gt2009
2009-05-27 01:34:28 | The correct answer (B) is a helix. Cycloid motion would be (E), which is wrong.
claire
2009-10-09 14:21:19 |
Both B and E are cycloid, e is just a special case.
The problem states "a positively charged particle is moving in the xy-plane." The motion is in the xy plane, and thus cannot be a helix (which requires motion in all 3 directions)
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|  | PhyAnnie
2008-11-04 06:07:49 | I was wondering... since the particle is always under the constant electric force of E*q upward, why the answer B doesn't show a upward trend, instead of being horizontal. That's strange.
f4hy
2009-04-03 19:13:19 |
It does seem strange, but it is the behavior when B and E are perpendicular. I don't remember which book but one makes this exact point when talking about cyclotrons.
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| | greed
2008-10-15 11:28:00 | Doesn't the cycloid motion correspond to a drift velocity that is proportional to  ? This would make the drift in the x direction, but choice D shows a drift in y. little confused ...
greed
2008-10-15 11:30:34 |
oops, never mind: just checked the answers
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| | cordercom
2008-10-05 17:58:59 | I think we can use the Poynting vector in this case. The net flux of energy density and hence the net trajectory of the particle must be in the direction of E cross B= (y X z)=x. So, the net displacement of the particle must be toward the right. Answer (B) seems most appropriate.
See Griffiths, Intro to Electrodynamics 3rd Edition, pg 206 & 347
physicsisgod
2008-10-30 16:34:35 |
The Poynting vector describes the direction of energy propogation for the EM field. It says nothing about the energy of particles moving in the EM field. This is a lucky coincidence.
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| | buddy.epson
2006-10-14 14:27:13 | the +z direction is determined by the cross product of +x and +y (aka the right-hand-rule). | | andreas
2005-11-10 05:00:51 | And for those who, like me, are confused by conventions, the magnetic field in the +z direction means it comes out of the page.
(I'm used to defining +z to be away from the observer, i.e. into the page)
shafatmubin
2009-11-05 14:13:55 |
Use cross product: i x j = k
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