Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
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Chapter 26, Problem 64AP
To determine
The maximum potential difference between wire and the cylinder.
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Assume that the internal diameter of the Geiger– Mueller tube described 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 106 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.
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 3.40 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 1.30 106 V/m. Use the equation
2?rℓE =
qin
?0
to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas.
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 1.95 cm and that the wire along the axis has a diameter of 0.210 mm. The dielectric strength of the gas between the central wire and the cylinder is 1.30 106 V/m. Use the equation 2?rℓE =qin/?0 to calculate the maximum potential difference that can be applied between the wire and the cylinder before breakdown occurs in the gas.
[Image]
A cross-section of a Geiger-Mueller tube shows an inner anode of radius rb and charge density ? and an outer cathode of radius ra and charge density −?.
Chapter 26 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 26.1 - A capacitor stores charge Q at a potential...Ch. 26.2 - Many computer keyboard buttons are constructed of...Ch. 26.3 - Two capacitors are identical. They can be...Ch. 26.4 - You have three capacitors and a battery. In which...Ch. 26.5 - If you have ever tried to hang a picture or a...Ch. 26 - Prob. 1OQCh. 26 - Prob. 2OQCh. 26 - Prob. 3OQCh. 26 - Prob. 4OQCh. 26 - Prob. 5OQ
Ch. 26 - Prob. 6OQCh. 26 - Prob. 7OQCh. 26 - Prob. 8OQCh. 26 - Prob. 9OQCh. 26 - Prob. 10OQCh. 26 - Prob. 11OQCh. 26 - Prob. 12OQCh. 26 - Prob. 13OQCh. 26 - Prob. 14OQCh. 26 - Prob. 1CQCh. 26 - Prob. 2CQCh. 26 - Prob. 3CQCh. 26 - Explain why a dielectric increases the maximum...Ch. 26 - Prob. 5CQCh. 26 - Prob. 6CQCh. 26 - Prob. 7CQCh. 26 - Prob. 8CQCh. 26 - (a) When a battery is connected to the plates of a...Ch. 26 - Two conductors having net charges of +10.0 C and...Ch. 26 - Prob. 3PCh. 26 - An air-filled parallel-plate capacitor has plates...Ch. 26 - Prob. 5PCh. 26 - Prob. 6PCh. 26 - When a potential difference of 150 V is applied to...Ch. 26 - Prob. 8PCh. 26 - Prob. 9PCh. 26 - Prob. 10PCh. 26 - Prob. 11PCh. 26 - Review. A small object of mass m carries a charge...Ch. 26 - Prob. 13PCh. 26 - Prob. 14PCh. 26 - Find the equivalent capacitance of a 4.20-F...Ch. 26 - Given a 2.50-F capacitor, a 6.25-F capacitor, and...Ch. 26 - Prob. 17PCh. 26 - Prob. 18PCh. 26 - Prob. 19PCh. 26 - Prob. 20PCh. 26 - A group of identical capacitors is connected first...Ch. 26 - Prob. 22PCh. 26 - Four capacitors are connected as shown in Figure...Ch. 26 - Prob. 24PCh. 26 - Prob. 25PCh. 26 - Prob. 26PCh. 26 - Two capacitors give an equivalent capacitance of...Ch. 26 - Prob. 28PCh. 26 - Prob. 29PCh. 26 - Prob. 30PCh. 26 - Prob. 31PCh. 26 - A 3.00-F capacitor is connected to a 12.0-V...Ch. 26 - Prob. 33PCh. 26 - Prob. 34PCh. 26 - Prob. 35PCh. 26 - Two identical parallel-plate capacitors, each with...Ch. 26 - Two capacitors, C1 = 25.0 F and C2 = 5.00 F, are...Ch. 26 - A parallel-plate capacitor has a charge Q and...Ch. 26 - Prob. 39PCh. 26 - Prob. 40PCh. 26 - Prob. 41PCh. 26 - Prob. 42PCh. 26 - Prob. 43PCh. 26 - Prob. 44PCh. 26 - Determine (a) the capacitance and (b) the maximum...Ch. 26 - Prob. 46PCh. 26 - Prob. 47PCh. 26 - Prob. 48PCh. 26 - Prob. 49PCh. 26 - Prob. 50PCh. 26 - An infinite line of positive charge lies along the...Ch. 26 - Prob. 52PCh. 26 - Prob. 53PCh. 26 - Prob. 54APCh. 26 - Prob. 55APCh. 26 - Prob. 56APCh. 26 - A uniform electric field E = 3 000 V/m exists...Ch. 26 - Prob. 58APCh. 26 - Prob. 59APCh. 26 - Why is the following situation impossible? A...Ch. 26 - Prob. 61APCh. 26 - A parallel-plate capacitor with vacuum between its...Ch. 26 - Prob. 63APCh. 26 - Prob. 64APCh. 26 - Prob. 65APCh. 26 - (a) Two spheres have radii a and b, and their...Ch. 26 - Prob. 67APCh. 26 - A parallel-plate capacitor of plate separation d...Ch. 26 - Prob. 69APCh. 26 - Prob. 70APCh. 26 - To repair a power supply for a stereo amplifier,...Ch. 26 - Prob. 72CPCh. 26 - Prob. 73CPCh. 26 - Consider two long, parallel, and oppositely...Ch. 26 - Prob. 75CPCh. 26 - Prob. 76CPCh. 26 - Prob. 77CPCh. 26 - Prob. 78CP
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- (a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ( 3.0 106 V/m) if the plates are separated by 2.00 mm and a potential difference of 5.0 103 V is applied? (b) How close together can the plates be with this applied voltage?arrow_forwardA pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?arrow_forwardA parallel-plate capacitor filled with air carries a charge Q. The battery is disconnected, and a slab of material with dielectric constant = 2 is inserted between the plates. Which of the following statements is true? (a) The voltage across the capacitor decreases by a factor of 2. (b) The voltage across the capacitor is doubled. (c) The charge on the plates is doubled. (d) The charge on the plates decreases by a factor of 2. (e) The electric field is doubled.arrow_forward
- A parallel-plate capacitor has square plates of side s = 2.50 cm and plate separation d = 2.50 mm. The capacitor is charged by a battery to a charge Q = 4.00 C, after which the battery is disconnected. A porcelain dielectric ( = 6.5) is then inserted a distance y = 1.00 cm into the capacitor (Fig. P27.88). Hint: Consider the system as two capacitors connected in parallel. a. What is the effective capacitance of this capacitor? b. How much energy is stored in the capacitor? c. What are the magnitude and direction of the force exerted on the dielectric by the plates of the capacitor? Figure P27.88arrow_forwardA parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0 cm2. The plates are charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water. Assume the liquid is an insulator. Determine (a) the charge on the plates before and after immersion, (b) the capacitance and potential difference after immersion, and (c) the change in energy of the capacitor.arrow_forwardAn election enters a region between two large parallel plates made of aluminum separated by a distance of 2.0 cm and kept at a potential difference of 200 V. The electron enters through a small hole in the negative plate and moves toward the positive plate. At the time the electron is near the negative plate, its speed is 4.0103 m/s. Assume the electric field between the plates to be uniform, and find the speed of electron at (a) 0.10 cm, (b) 0.50 cm, (c) 1.0 cm, and (d) 1.5 cm from the negative plate, and (e) immediately before it hits the positive plate.arrow_forward
- An arrangement of capacitors is shown in Figure P27.23. a. If C = 9.70 105 F, what is the equivalent capacitance between points a and b? b. A battery with a potential difference of 12.00 V is connected to a capacitor with the equivalent capacitance. What is the energy stored by this capacitor? Figure P27.23 Problems 23 and 24.arrow_forwardA large parallel-plate capacitor is attached to a battery that has terminal potential (Fig. 27.15A). After a period of time, the capacitor stores charge Q so that its top plate is positive and its bottom plate is negative, and the potential difference between the plates is VC = . An I-shaped neutral conductor consisting of two parallel plates connected by a wire is slipped between the plates of the capacitor so that all four plates are parallel (Fig. 27.15B). What are the charges q1, and q2 on the plates of the I-shaped conductor? What is the potential difference VC between the top and bottom plates of the capacitor?arrow_forwardFind the equivalent capacitance for the network shown in Figure P27.26 if C1 = 1.00 F, C2 = 2.00 F, C3 = 3.00 F, C4 = 4.00 F, and C5 = 5.00 F. FIGURE P27.26 Problems 26 and 27.arrow_forward
- (a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is 3.00106 V/m, if the plates are separated by 2.00 mm and a potential difference of 5.010V is applied? (b) How close together can the plates be with this applied voltage?arrow_forwardFor the four capacitors in the circuit shown in Figure P27.30, CA = 1.00 F, CB = 4.00 F, CC = 2.00 F, and CD = 3.00 F. What is the equivalent capacitance between points a and b? Figure P27.30arrow_forwardA Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.arrow_forward
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