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muonneutrino91
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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