A detector of radiation called a Geiger tube consists of a closed, hollow, conducting cylinder with a fine wire along its axis. Suppose that the internal diameter of the cylinder is 2.50 cm and that the wire along the axis has a diameter of 0.200 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.20 Ă— 10^6 V/m. Calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas.
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50 \, \text{cm} = 0.025 \, \text{m} \) - Diameter of the wire, \( d = 0.200 \, \text{mm} = 0.0002 \, \text{m} \) - Dielectric strength of the gas, \( E_{\text{max}} = 1.20 \times 10^6 \, \text{V/m} \) Show more…
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A Geiger-Mueller tube is a radiation detector that consists of a closed, hollow, metal cylinder (the cathode) of inner radius ra and a coaxial cylindrical wire (the anode) of radius rb (see figure below) with a gas filling the space between the electrodes. Assume that the internal diameter of a Geiger-Mueller tube is 1.55 cm and that the wire along the axis has a diameter of 0.205 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.25 106 V/m. Use the equation 2?râ„“E = qin ?0 to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas.
Timothy J.
Assume that the internal diameter of the Geiger-Mueller tube described in Problem 42 in Chapter 24 is 2.50 cm and that the wire along the axis has a diameter of 0.200 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.20 x 10^6 V/m. Use the result of that problem to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas.
Kratika B.
A Geiger tube is a radiation detector that essentially consists of a closed, hollow metal cylinder (the cathode) of inner radius $r_{a}$ and a coaxial cylindrical wire (the anode) of radius $r_{b}$ (Fig. P25.61). The charge per unit length on the anode is $\lambda,$ while the charge per unit length on the cathode is $-\lambda .$ A gas fills the space between the electrodes. When a high-energy elementary particle passes through this space, it can ionize an atom of the gas. The strong electric field makes the resulting ion and electron accelerate in opposite directions. They strike other molecules of the gas to ionize them, producing an avalanche of electrical discharge. The pulse of electric current between the wire and the cylinder is counted by an external circuit. (a) Show that the magnitude of the potential difference between the wire and the cylinder is $$ \Delta V=2 k_{e} \lambda \ln \left(\frac{r_{a}}{r_{b}}\right) $$ (b) Show that the magnitude of the electric field in the space between cathode and anode is given by $$ E=\frac{\Delta V}{\ln \left(r_{a} / r_{b}\right)}\left(\frac{1}{r}\right) $$ where $r$ is the distance from the axis of the anode to the point where the field is to be calculated.
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