Chapter 7, Problem 71P

In a Geiger counter, a thin metallic wire at the center of a metallic tube is kept at a high voltage with respect to the metal tube. Ionizing radiation entering the tube knocks elections off gas molecules or sides of the tube that then accelerate towards the center wire, knocking off even more electrons. This process eventually leads to an avalanche that is detectable as a current. A particular Geiger counter has a tube of radius K and the inner wire of radius a is at a potential of V₀ volts with respect to the outer metal tube. Consider a point P at a distance s from tine center wire and far away from the ends, (a) Find a formula for the electric field at a point P inside using tine infinite wire approximation, (b) Find a formula for the electric potential at a point P inside. (c) Use V₀ = 900 V, a = 3.00 min. P = 2.00 cm, and find the value of the electric field at a point 1.00 cm from the center.