![Fundamentals of Physics, Volume 1, Chapter 1-20](https://www.bartleby.com/isbn_cover_images/9781118233764/9781118233764_largeCoverImage.gif)
Concept explainers
A cylindrical capacitor has radii a and b as in Fig. 25-6. Show that half the stored electric potential energy lies within a cylinder whose radius is
Figure 25-6 A cross section of a long cylindrical capacitor, showing a cylindrical Gaussian surface of radius r (that encloses the positive plate) and the radial path of integration along which Eq.25-6 is to be applied.This figure also serves to illustrate a spherical capacitor in a cross section through its center.
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 25 Solutions
Fundamentals of Physics, Volume 1, Chapter 1-20
Additional Science Textbook Solutions
Mathematical Methods in the Physical Sciences
Conceptual Physical Science (6th Edition)
Physics: Principles with Applications
Essential University Physics (3rd Edition)
University Physics Volume 1
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
- A spherical capacitor is formed from two concentric spherical conducting spheres separated by vacuum. Tire inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is applied to the capacitor, (a) What is the capacitance of the capacitor? tb) What is the magnitude of the electrical field at r = 12.6 cm, just outside the inner sphere? (c) What is the magnitude of the electrical field at r = 14.7 cm, just inside the outer sphere? (d) For a parallel-plate capacitor the electrical field is uniform in the region between the plates, except near the edges of the plates. Is this also true for a spherical capacitor?arrow_forwardHow many electrons should be removed from an initially uncharged spherical conductor of radius 0.300 m to produce a potential of 7.50 kV at the surface?arrow_forwardAccording to UE=12C(V)2 (Eq. 27.3), a greater capacitance means more energy is stored by the capacitor, but according to UE = Q2/2C (Eq. 27.2), a greater capacitance means less energy is stored. How can both of these equations be correct?arrow_forward
- An 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_forwardIn a certain region of space, the electric field is zero. From this fact, what can you conclude about the electric potential in this region? (a) It is zero, (b) It does not vary with position. (c) It is positive. (d) It is negative. (e) None of those answers is necessarily true.arrow_forwardA spherical capacitor is formed from two concentric spherical conducting shells separated by a vacuum. The inner sphere has radius 12.5 cm and the outer sphere has radius 14.8 cm. A potential difference of 120 V is appLied to the capacitor, (a) What is the energy density at r = 12.6 cm, just outside the inner sphere? (b) What is the energy density at r = 14.7 cm, just inside the outer sphere? (c) For the parallel-plate capacitor the energy density is uniform in the region between the plates, except near the edges of the plates. Is this also true for the spherical capacitor?arrow_forward
- (a) Find the potential difference VB required to stop an electron (called a slopping potential) moving with an initial speed of 2.85 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, Vp/Ve. The answer should be in terms of the proton mass mp and electron mass me.arrow_forwardA 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_forward(a) Find the potential difference VB required to stop an electron (called a slopping potential) moving with an initial speed of 2.85 107 m/s. (b) Would a proton traveling at the same speed require a greater or lesser magnitude potential difference? Explain. (c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, Vp/Ve. The answer should be in terms of the proton mass mp and electron mass me.arrow_forward
- (i) Rank the following five capacitors from greatest to smallest capacitance, noting any cases of equality, (a) a 20-F capacitor with a 4-V potential difference between its plates (b) a 30-F capacitor with charges of magnitude 90 C on each plate (c) a capacitor with charges of magnitude 80 C on its plates, differing by 2 V in potential. (d) a 10-F capacitor storing energy 125 J (e) a capacitor storing energy 250 J with a 10-V potential difference (ii) Rank the same capacitors in part (i) from largest to smallest according to the potential difference between the plates, (iii) Rank the capacitors in part (i) in the order of the magnitudes of the charges on their plates, (iv) Rank the capacitors in part (i) in the order of the energy they store.arrow_forward(a) Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P16.46 if C1 = 5.00 F, C2 = 10.00 F, and C3 = 2.00 F. (b) If the potential between points a and b is 60.0 V, what charge is stored on C5? Figure P16.46arrow_forwardA 56.90-pF cylindrical capacitor carries a charge of 1.540 C. The capacitor has a length of 1.000 103 m. a. What is the potential difference across the capacitor? b. If the radial separation between the two cylinders is 6.520 104 m, what are the inner and outer radii of the cylindrical conductors?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- College PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133939146/9781133939146_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133104261/9781133104261_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305116399/9781305116399_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781938168161/9781938168161_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285737027/9781285737027_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif)