10. The radius of internal and external conductor of a spherical capacitor are a and b respectively. The dielectric constant of the dielectric in the middle is. If the voltage applied between the two poles is U, 1) Calculate the electric field intensity of each point in the capacitor and the charge on the electrode. 2) Calculate the capacitance and electrostatic energy of the capacitor. U

10. The radius of internal and external conductor of a spherical capacitor are a and b respectively. The dielectric constant of the dielectric in the middle is. If the voltage applied between the two poles is U, 1) Calculate the electric field intensity of each point in the capacitor and the charge on the electrode. 2) Calculate the capacitance and electrostatic energy of the capacitor. U

Physics for Scientists and Engineers

10th Edition

ISBN:9781337553278

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter25: Capacitance And Dielectrics

Section: Chapter Questions

Problem 37AP: A parallel-plate capacitor with vacuum between its horizontal plates has a capacitance of 25.0 F. A...

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In different experimental trials, an electron, a proton, or a doubly charged oxygen atom (O--), is fired within a vacuum tube. The particle's trajectory carries it through a point where the electric potential is 40.0 V and then through a point at a different potential. Rank each of the following cases according to the change in kinetic energy of the particle over this part of its flight from the largest increase to the largest decrease in kinetic energy. In your ranking, display any cases of equality, (a) An electron moves from 40.0 V to 60.0 V. (b) An electron moves front 40.0 V to 20.0 V. (c) A proton moves from 40.0 V to 20.0 V'. (d) A proton moves from 40.0 V to 10.0 V. (e) An O-- ion mines from 40.0 V to 60.0 V.
For a Teflon ™-filled, parallel-plate capacitor, the area of the plate is 50.0 cm and the spacing between the plates is 0.50 mm. If the capacitor is connected to a 200-V battery, find (a) the free charge on the capacitor plates, (b) the electrical field in the dielectric, and (c) the induced charge on the dielectric surfaces.
Integrated Concepts (a) What voltage will accelerate electrons to a speed of 6.00107m/s ? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.
a parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a 6.00-V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? (d) Find the magnitude of the charge density on each plate. (e) Without disconnecting the battery, the plates are moved farther apart. Qualitatively, what happens to each of the previous answers?
An air-filled (empty) parallel-plate capacitor is made from two square plates that are 25 cm on each side and 1.0 mm apart. The capacitor is connected to a 50-V battery and fully charged. It is then disconnected from the battery and its plates are pulled apart to a separation of 2.00 mm. (a) What is the capacitance of this new capacitor? (b) What is the charge on each plate? (c) What is the electrical field between the plates?
A simple and common technique for accelerating electrons is shown in Figure 18.55, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electorn if the field strength is 2.50104 N/C. (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.
A parallel-plate capacitor with plates of area LW and plate separation t has the region between its plates filled with wedges of two dielectric materials as shown in Figure P25.48. Assume t is much less than both L and W. (a) Determine its capacitance. (b) Should the capacitance be the same if the labels 1 and 2 are interchanged? Demonstrate that your expression does or does not have this property. (c) Show that if 1 and 2 approach equality to a common value , your result becomes the same as the capacitance of a capacitor containing a single dielectric: C = 0LW/t. Figure P25.48
Unreasonable Results (a) A certain parallel plate capacitor has plates of area 4.00 m2 separated by 0.0100 mm of nylon, and stores 0.170 C of charge. What is the applied voltage? (b) What is unreasonable about this result? (c) Which assumptions are responsible or inconsistent?
A capacitor is constructed from two square, metallic plates of sides and separation d. Charges +Q and Q are placed on the plates, and the power supply is then removed. A material of dielectric constant is inserted a distance x into the capacitor as shown in Figure P25.49 (page 690). Assume d is much smaller than x. (a) Find the equivalent capacitance of the device. (b) Calculate the energy stored in the capacitor. (c) Find the direction and magnitude of the force exerted by the plates on the dielectric. (d) Obtain a numerical value for the force when x = /2, assuming = 5.00 cm, d = 2.0 mm, the dielectric is glass ( = 4.50), and the capacitor was charged to 2.00 103 V before the dielectric was inserted. Suggestion: The system can be considered as two capacitors connected in parallel. Figure P25.49
A GeigerMueller 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 (Fig. P24.42a). The charge per unit length on the anode is , and the charge per unit length on the cathode is . A gas fills the space between the electrodes. When the tube is in use (for example, in measuring radioactivity from fruit in Fig. P24.42b) and 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 electric potential difference between the wire and the cylinder is V2keln(rarb) (b) Show that the magnitude of the electric field in the space between cathode and anode is E=Vln(ra/rb)(1r) where r is the distance from the axis of the anode to the point where the field is to be calculated. Figure P24.42
A variable air capacitor used in a radio tuning circuit is made of N semicircular plates, each of radius R and positioned a distance d from its neighbors, to which it is electrically connected. As shown in Figure P25.5, a second identical set of plates is enmeshed with the first set. Each plate in the second set is halfway between two plates of the First set. The second set can rotate as a unit. Determine the capacitance as a function of the angle of rotation , where = 0 corresponds to the maximum capacitance. Figure P25.5
a parallel-plate capacitor with area 0.200 m2 and plate separation of 3.00 mm is connected to a 6.00-V battery. (a) What is the capacitance? (b) How much charge is stored on the plates? (c) What is the electric field between the plates? (d) Find the magnitude of the charge density on each plate. (e) Without disconnecting the battery, the plates are moved farther apart. Qualitatively, what happens to each of the previous answers?