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Homework Help: Volume Charge Density of Proton Beam

  1. Dec 27, 2015 #1
    1. The problem statement, all variables and given/known data
    1.0 mA proton beam accelerated through potential difference of 1 keV.
    Determine the volume charge density of the beam after acceleration assuming uniform current distribution within diameter of 5mm, with zero current outside of this.
    Particle starting from rest.

    Final answer I get is out by 10-4 to the solution given in my notes. Pretty certain its a mistake in the notes, somebody seconding this would give me peace at mind.

    2. Relevant equations
    ρ = I/νA
    W = qV

    ρ = charge density,
    A = surface area of beam,
    I = beam current,
    v = proton velocity,
    W = work
    V = voltage

    3. The attempt at a solution
    W = 1.6x10-16 J = KEfinal (since starting from rest)

    ∴ 2W/mproton = v2
    ∴ v ≈4.4x105

    A = π 6.25x10-6 m2

    ∴ ρ = 0.001 / π.(6.25x10-6).4.4x105 ≈1.1x10-4
  2. jcsd
  3. Dec 27, 2015 #2
    Hi, I just worked through the problem and obtained the same result as you, assuming your answer is in units of coulombs/cubic metre.
  4. Dec 29, 2015 #3
    Thanks, TonyS.
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