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 electrons 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 R and the inner wire of radius a is at a potential of Vo volts with respect to the outer metal tube. Consider a point P at a distance s from the center wire and far away from the ends.
a. Use Vo = 900 Va = 3.00 mm, R = 2.00 cm, and find the value of the electric potential at a point 1.00 cm from the center of the wire (with respect to the outer metal tube).
b. Find a formula for the electric potential at a point P inside.
c. Use Vo = 900 V, a = 3.00 mm, R = 2.00 cm, and find the value of the electric field at a point 1.00 cm from the center.