A simple Geiger counter is constructed out of a setup similar to what we just
used in problem 5. A thin wire with a linear charge density _ is held in the
center of a cylindrical tube, which is filled with an inert gas. When a high speed
particle coming from a radioactive decay, cosmic ray, etc. enters the gas-filled
tube, collisions with the gas knock electrons off of their atoms. The free electrons
then accelerate towards the positively charged wire, and collide with other gas
atoms causing them to lose electrons as well. This leads to a cascade of electrons
accelerating towards the wire, which will be turned into a measurable current
upon reaching the wire. For this problem, the tube has a radius of 1cm and is
10cm long; the wire has a radius of 10_m and _ = 108C=m.
(a) What is the force on a free electron located at the outer wall of the tube?
(b) What is the force on an electron immediately next to the thin wire?
(c) What is the work done on an electron pulled from the outer wall of the tube
to the wire?
(d) Calculate the electric flux through the walls of the tube perpendicular to the
wire (i.e. the walls the wire is attached to).
(e) Calculate the electric flux through the surface of the tube parallel to the
wire. Would this value change if the Geiger counter were box shaped rather