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

• imy786

## 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.

## 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 ${\vec A} \cdot ({\vec A} \times {\vec B}) = 0$ 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 $v \leq E/B$ as stated.

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

Regards

so why do you think is introductory level.

What level do you think this is? college/ high school/under/ grad/phd?