# Volume Charge Density of Proton Beam

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1. Dec 27, 2015

### muonneutrino91

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. Dec 27, 2015

### TonyS

Hi, I just worked through the problem and obtained the same result as you, assuming your answer is in units of coulombs/cubic metre.

3. Dec 29, 2015

### muonneutrino91

Thanks, TonyS.