1. The problem statement, all variables and given/known data A 1.0 μA proton beam is accelerated across a potential difference of 1.0 kV. Assume the beam has uniform current density over a diameter of 2.0 mm, and zero outside. Find: volume charge density in the beam, (HINT use λ=I/v where λ= charge/ unit length) The radial electric field intensity inside and outside of the beam. 2. Relevant equations λ=I/v, λ=Q/unit length, ρ_v=Q_total/V, KE=1/2mv^2 3. The attempt at a solution I approached the first part by finding kinetic energy using know values for mass and charge then rearranging to find velocity. I then inserted velocity into the hint equation to find total charge then used volume density= total charge over potential difference. However I don't think this last approach is correct. For the second question I'm so confused. I know E=-∇V but V is a scalar so my other approach was to show that it had zero electric field due to no charge. Any help would be so appreciated! Thanks!