Volume Charge Density of Proton Beam

[muonneutrino91]

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 = KE_final (since starting from rest)

∴ 2W/m_proton = v²
∴ v ≈4.4x10⁵

A = π 6.25x10^-6 m²

∴ ρ = 0.001 / π.(6.25x10^-6).4.4x10⁵ ≈1.1x10^-4

 

[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.

 

[muonneutrino91]

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.