The figure shows a Geiger counter, a device used to detect ionizing radiation (r
ID: 1528150 • Letter: T
Question
The figure shows a Geiger counter, a device used to detect ionizing radiation (radiation that causes ionization of atoms). The counter consists of a thin, positively charged central wire surrounded by a concentric, circular, conducting cylindrical shell with an equal negative charge. Thus, a strong radial electric field is set up inside the shell. The shell contains a low-pressure inert gas. A particle of radiation entering the device through the shell wall a few of the gas atoms. The resulting free electrons (e) are drawn to the positive wire. However, the electric field is so intense that, between collisions with gas atoms, the free electrons gain energy sufficient to ionize these atoms also. More free electrons are thereby created, and the process is repeated until the electrons reach the wire. The resulting "avalanche" of electrons is collected by the wire, generating a signal that is used to record the passage of the original particle of radiation. Suppose the radius of the central wire is 24 um, the inner radius of the shell 1.8 cm, and the length of the shell 13 cm. If the electric field at the shell's inner wall is 2.4 times 10^4 N/C, what is the total positive charge on the central wire?Explanation / Answer
The field of this setup will be radially outwards from the cnteral wire. We need to know the magnitude of field in between, that variate with the distance r. The field of the cylinder is known so we can use the gauss law to find the charge.
the only charge that is on the wire enclosed by the Gaussian surface, we denote it by q. The area of the surface is 2piRL and flux is phi = 2 pi R L E.
Let us assume there is no flux through the ends of the cylinder, so this phi is the total flux.
From Gauss law,
q = 2 pi epsilon0 R L E
q = 2 x 3.14 x 8.85 x 10^-12 x 0.018 x 0.13 x 2.4 x 10^4 = 3.12 x 10^-9 C
Hence, q = 3.12 x 10^-9 C
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