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Homework Help: Drift speed of a particle in

  1. Oct 4, 2007 #1
    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 mass m and positive charge q moves in uniform electric and magnetic fields, E pointing in the y direction and B in the z direction (an arrangement called "crossed E and B fields"). Suppose the particle is initially at the origin and is given a kick at time t=0 along the x axis with v[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 plane z=0 (done)

    (b) Prove that there is a unique value of v[tex]_{x0}[/tex], called the drift speed v[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 whole z=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 get v[tex]_{x}[/tex]=0 but I know that is wrong. Did I go about this the wrong way??
     
  2. jcsd
  3. Oct 4, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    E is in the y direction. So is vxB, since v is along x and B is along z. You just have to pick an absolute value of v so the total of all the forces, E+vxB=0.
     
  4. Oct 5, 2007 #3
    shoot I missed the E in the y direction in my equations for a)!! Thanks!!!!!!!!!!
     
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