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What B-field is required so that the protons are not deflected?

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data
    A proton that is accelerated from rest through a potential of 20.0 kV enters the velocity filter, consisting of a parallel-plate capacitor and a magnetic field, shown below.
    The E-field between the parallel capacitor plates is 5.9x105 N/C. What B-field is required so that the protons are not deflected?

    2. Relevant equations
    he protons entering the region of the electric field E will experience a force directed downward with magnitude:

    z*E, where z = +1 elementary charge

    The protons will also experience a force due to the magnetic field of magnitude:


    where v is the speed of the protons. The direction of this force is given by the right hand rule, so for a magnetic field directed into the page, this force is directed toward the top of the page.

    When these forces are equal in magnitude, then the proton will pass undeflected through the velocity filter. The condition of interest is then:

    z*v*B = z*E

    B = E/v

    To find the speed of the protons, we need to calculate their kinetic energy:

    (1/2)*m*v^2 = z*V,

    where V is the accelerating voltage, so

    v = sqrt(2*z*V/m)

    B = E/sqrt(2*z*V/m)

    E = 5.9*10^5 N/C
    z = 1.602*10^-19 C
    V = 20*10^3 V
    m = ?

    3. The attempt at a solution
    I am just really confused on how to find what m is since i dont know what v is? like i know the big V but not the little v.
  2. jcsd
  3. Mar 16, 2009 #2
    Can't you just use the fact that the mass of the proton is 1.67x10^-27 kg? It doesn't seem you're supposed to solve for this.

    I don't think the velocity matters in this case, because no matter what velocity the protons are traveling at, they will either feel a deflection or not.
  4. Mar 16, 2009 #3
    hahaha, so i accidentially did 301 T insead of .301 T and that was y i was getting it wrong. like i had through that it was just the mass of the proton but since i got it wrong i figured my mass was wrong. thanks though dude
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