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## Homework Statement

A detector of radiation called a Geiger-Muller counter consists of a closed, hollow, conducting cylinder with a fine wire along its axis. Suppose that the internal diameter of the cylinder is 3.00 cm and that the wire along the axis has a diameter of 0.2 mm. If the dielectric strength of the gas between the central wire and the cylinder is 1.00 ✕ 106 V/m, calculate the maximum voltage that can be applied between the wire and the cylinder before breakdown occurs in the gas.

## Homework Equations

E=-∫Vds

∫EdA = Qenc/ε0

## The Attempt at a Solution

Since the electric field is not constant between the cylinder and the wire, I tries to derive for the electric field using Gauss' law from the wire to the cylinder using radius 1.5e-2m and 0.1e-3m. However the equation comes out like Q/(2πlε0)ln(r). l is for the length of the gaussian surface which i don't know and i don't see anywhere that I can cancel l . Besides, I have no idea where I can use that dielectric strength since electric field vary.