(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am working on a problem and don't know if I am going about it right because I am stuck.

A charged particle of massmand positive chargeqmoves in uniform electric and magnetic fields,Epointing in theydirection andBin thezdirection (an arrangement called "crossed E and B fields"). Suppose the particle is initially at the origin and is given a kick at timet=0 along thexaxis withv[tex]_{}x[/tex]=v[tex]_{x0}[/tex] (positive or negative). (those are supposed to be subscripts but I can't get it to work)

(a)Write down the equation of motion for the particle and resolve it into it's three components. (done) Show that the motion remains in the planez=0 (done)

(b)Prove that there is a unique value ofv[tex]_{x0}[/tex], called the drift speedv[tex]_{dr}[/tex],for which the particle moves undeflected through the fields. (This is what I can't get)

2. Relevant equations

F=ma

F=q(E+vXB)

3. The attempt at a solution

I wrote down the equation of motion and when separated I got

v[tex]_{y}[/tex]*B[tex]_{z}[/tex]=m*dv[tex]_{x}[/tex]/dt

v[tex]_{x}[/tex]*B[tex]_{z}[/tex]=m*dv[tex]_{y}[/tex]/dt

0=m*dv[tex]_{z}[/tex]/dt

I proved the wholez=o plane thing.

Now I get to b

Iknow that x(t)=f some arbitrary function and y(t)=0. (We already know z(t)=0). So I used the second equation above and solve it to get y(t)=(v[tex]_{x}[/tex]*B[tex]_{z}[/tex]*t^2)/2m=0. Ok so what do I do from here. I am lost I can divide everything and getv[tex]_{x}[/tex]=0 but I know that is wrong. Did I go about this the wrong way??

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Drift speed of a particle in

**Physics Forums | Science Articles, Homework Help, Discussion**