Volume Charge Density of Proton Beam

  • #1

Homework Statement


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.

Homework Equations


ρ = I/νA
W = qV

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

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
 

Answers and Replies

  • #2
21
6
Hi, I just worked through the problem and obtained the same result as you, assuming your answer is in units of coulombs/cubic metre.
 
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Likes muonneutrino91
  • #3
Hi, I just worked through the problem and obtained the same result as you, assuming your answer is in units of coulombs/cubic metre.
Thanks, TonyS.
 

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