A beam of 9.5 MeV electrons (gamma = 20) amounting as a current to 0.05 microamperes, is traveling through a vacuum. The transverse dimensions of the beam are less than 1 mm, and there are no positive charges in or near it.
(a) In the lab frame, what is approximately the electric field strength 1cm away from the beam, and what is the average distance between an electron and the next one ahead of it, measured parallel to the beam?
(b) answer the same question for the electron rest frame.
The Attempt at a Solution
I used kinetic energy to find the electric field, so i did something like this:
K = .5mv^2 = eV = eEd, where m was the mass of the electron, v was its velocity, e is the electron charge, E is the electric field strength, and d is the distance away from it. V is voltage. I ended up with something like this:
E = (mv^2)/(2ed) = 2.55 x 10^7 V/m (velocity was found using gamma).
I'm having a little bit more trouble with the interelectron difference, though. I'm just stuck. Can anyone just give me a hint to get me started?