Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 24, Problem 49P
(a)
To determine
To Show: The capacitance of spherical capacitor is
(b)
To determine
To Show: The capacitance of the spherical capacitor is
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A spherical capacitor consists of a spherical conducting shell of radius b and charge 2Q concentric with a smaller conductingsphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radius b of the outer sphere approaches infinity,the capacitance approaches the value a/ke = 4πεoa.
A spherical conductor of radius a and charge Q is concentric with spherical shell of negligible thickness, radius b > a, and charge -Q (as shown in the figure). Show that the capacitance of this cylindrical capacitor is
C = 4πɛ0 ab/b-a
A spherical capacitor consists of a spherical conducting shell of radius b and charge − Q concentric with a smaller conducting sphere of radius a and charge Q. (a) Find the capacitance of this device. (b) Show that as the radiusb of the outer sphere approaches infinity, the capacitance approaches the value a/ ke = 4πϵ0a.
Chapter 24 Solutions
Physics for Scientists and Engineers
Ch. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6PCh. 24 - Prob. 7PCh. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10P
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- Check Your Understanding The radius of the outer sphere of a spherical capacitor is five times the radius of its inner shell. What are the dimensions of this capacitor if its capacitance is 5.00 pF?arrow_forwardCheck Your Understanding When a cylindrical capacitor is given a charge of 0.500 nC, a potential difference of 20.0 V is measured between the cylinders, (a) What is the capacitance of this system? (b) If the cylinders are 1.0 m long, what is the ratio of their radii?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
- Check Your Understanding The capacitance of a parallel-plate capacitor is 2.0 pF. If the area of each plate is 2.4 cm2, what is the plate separation?arrow_forwardCheck Your Understanding The potential difference across a 5.0-pF capacitor is 0.40 V. (a) What is the energy stored in this capacitor? (b) The potential difference is now increased to 1.20 V. By what factor is the stored energy increased?arrow_forwardA parallel-plate capacitor with capacitance 5.0F is charged with a 12.0-V battery, after which the battery is disconnected. Determine the minimum work required to increase the separation between the plates by a factor of 3.arrow_forward
- When discharging a capacitor, as discussed in conjunction with Figure 21.39, how long does it take for the voltage on the capacitor to reach zero? Is this a problem?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_forwardCheck Your Understanding Repeat the calculations of Example 8.10 for the case in which the battery remains connected while the dielectric is placed in the capacitor.arrow_forward
- A spherical capacitor consists of a spherical conducting shell of radius b and charge 2Q that is concentric with a smaller conducting sphere of radius a and charge +Q (Fig. P20.36). (a) Show that its capacitance is C=abke(ba) (b) Show that as b approaches infinity, the capacitance approaches the value a/ke = 40a. Figure P20.36arrow_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_forwardWhen a Leyden jar is charged by a hand generator (Fig. 27.1, page 828), the work done by the person turning the crank is stored as electric potential energy in the jar. When a capacitor is charged by a battery, where does the electric potential energy come from?arrow_forward
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