Lorentz Force Part 2: Proving v.E = 0, E.B = 0, v ≥ E/B

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Homework Help Overview

The discussion revolves around the motion of a charged particle in the presence of uniform electric and magnetic fields. The original poster seeks to demonstrate specific relationships involving the velocity of the particle and the fields, specifically showing that the dot products of velocity with electric field and magnetic field are zero, and establishing a relationship between the velocity and the ratio of electric to magnetic field magnitudes.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of constant velocity on the forces acting on the charged particle. There are suggestions to approach the problem either conceptually, by considering the directions of forces, or algebraically, using vector identities. Questions arise regarding the classification of the problem's difficulty level.

Discussion Status

Some participants have provided guidance on how to approach the problem, suggesting both conceptual and algebraic methods. There is an ongoing exploration of the problem's classification in terms of educational level, with differing opinions on whether it is introductory or more advanced.

Contextual Notes

Participants note that the problem may be better suited for an introductory physics forum, indicating a potential mismatch in the expected complexity of the discussion.

imy786
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Homework Statement



The motion of a charged particle P, observed in an inertial frame S. It is found that P moves with constant velocity v through a region of space where there is a uniform electric field E and a uniform magnetic field B. The speed v = |v|and the field magnitudes E = |E| and B = |B| are all non-vanishing.

Show that v.E =0.

Show that E.B =0.

Show that v ≥ E/B.


dont know how to start this.Need help.
 
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imy786 said:

Homework Statement



The motion of a charged particle P, observed in an inertial frame S. It is found that P moves with constant velocity v through a region of space where there is a uniform electric field E and a uniform magnetic field B. The speed v = |v|and the field magnitudes E = |E| and B = |B| are all non-vanishing.

Show that v.E =0.

Show that E.B =0.

Show that v ≥ E/B.


dont know how to start this.Need help.

As someone told you in the other thread, the first thing to realize is what it means to say that the velocity is constant. What does it imply for the electric and magnetice force?

Then, to answer the first two questions, it is possible to either prove the answers using words only, by talking aboutthe direction of the forces and so on (using the fact that the magnetic force is always perpendicular to the velocity of the charge). Or they can be answered using algebra only and using the obvious identity [itex]{\vec A} \cdot ({\vec A} \times {\vec B}) = 0[/itex] for any two vectors A and B.
For the third question, just write the condition on the magnitudes of the forces and isolate v. The answer will contain a sin theta and since theta may vary from 0 to 180 degrees, you will find that [itex]v \leq E/B[/itex] as stated.

Btw, this should have been posted in the introductory physics forum, probably.

Regards
 
nrged- thanks for the advice,

so why do you think is introductory level.

What level do you think this is? college/ high school/under/ grad/phd?
 
imy786 said:
nrged- thanks for the advice,

so why do you think is introductory level.

What level do you think this is? college/ high school/under/ grad/phd?
This material is usually covered in high school physics and freshman year of college. Read some of the other advanced level threads for comparison.
 

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