A Geiger-Muller counter is a radiation detector that essentially consists of a h

Question

A Geiger-Muller counter is a radiation detector that essentially consists of a hollow cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius rb (Fig. P25.62). The charge per unit length on the anode is A, while the charge per unit length on the cathode is - lambda . Show that the magni-tude of the potential difference between the wire and the cylinder in the sensitive region of the detector is delta V = 2ke lambda ln (ra/rb) Show that the magnitude of the electric field over that region is given by delata E = V/In(ra/rb) (1/r) where r is the distance from the center of the anode to the point where the field is to be calculated.

Explanation / Answer

Choose the Gaussian 's surface as a cylider that have the length ofL and radius of R which shared the same mid line. We have Q/0=E*S Q=*l S=2R*l so E=/(20R)=k2/R Let V be the electric potential E*dr=-dV so -dV=k2*dr/r V=k2*ln(ra/rb) (magnitude) (ans) *, so we have k2=V/ln(ra/rb). E=k2/R=V/ln(ra/rb) *1/R

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