Concept explainers
A capacitor is constructed from two square, metallic plates of sides ℓ and separation d. Charges +Q and −Q are placed on the plates, and the power supply is then removed. A material of dielectric constant κ 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 = ℓ/2, assuming ℓ = 5.00 cm, d = 2.0 mm, the dielectric is glass (κ = 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)
The equivalent capacitance of the device.
Answer to Problem 49CP
The equivalent capacitance of the device is
Explanation of Solution
Given Info: The sides of the metallic plate is
The given Figure of the system is shown below.
Figure (1)
The system can be considered as two capacitors one with a dielectric and one without dielectric. The top plates of the two capacitors always have same potential
Formula to calculate the area of the with dielectric is,
Here,
Formula to calculate the capacitance with dielectric is,
Here,
Substitute
Formula to calculate the area of the without dielectric is,
Here,
Formula to calculate the capacitance without dielectric is,
Here,
Substitute
Since, the capacitors
Substitute
Conclusion:
Therefore, the equivalent capacitance of the device is
(b)
The energy stored in the capacitor.
Answer to Problem 49CP
The energy stored in the capacitor is
Explanation of Solution
Given Info: The sides of the metallic plate is
The equivalent capacitance of the device is,
Formula to calculate the energy stored in the capacitor is,
Substitute
Conclusion:
Therefore, the energy stored in the capacitor is
(c)
The magnitude and the direction of the force exerted by the plates on the dielectric.
Answer to Problem 49CP
The magnitude of the force exerted by the plates on the dielectric is
Explanation of Solution
Given Info: The sides of the metallic plate is
As, the dielectric slab is inserted the potential energy of the system is affected. The
Formula to calculate the force exerted by the plates on the dielectric is,
Here,
Substitute
The negative value of the force indicates the dielectric is pushed out from the capacitor.
Conclusion:
Therefore, the magnitude of the force exerted by the plates on the dielectric is
(d)
The magnitude of the force exerted by the plates on the dielectric.
Answer to Problem 49CP
The magnitude of the force exerted by the plates on the dielectric is
Explanation of Solution
Given Info: The sides of the metallic plate is
The distance of plate in the dielectric medium is,
Formula to calculate the charge is,
Here,
The magnitude of the force exerted by the plates on the dielectric is,
Here,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the magnitude of the force exerted by the plates on the dielectric is
Want to see more full solutions like this?
Chapter 25 Solutions
Physics for Scientists and Engineers with Modern Physics
Additional Science Textbook Solutions
Essential University Physics (3rd Edition)
University Physics Volume 1
Physical Science
EBK FUNDAMENTALS OF THERMODYNAMICS, ENH
MODERN PHYSICS (LOOSELEAF)
The Cosmic Perspective (8th Edition)
- 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_forwardThe separation between the 4.40-cm2 plates of an air-filled parallel-plate capacitor is 0.230 cm. a. What is the capacitance of this capacitor? If the capacitor is connected to a 9.00-V battery, find b. the charge stored by the capacitor and c. the magnitude of the electric field between its plates.arrow_forwardFigure P27.75 shows four capacitors with CA = 4.00 F, CB = 8.00 F. CC = 6.00 F. and CD = 5.00 F connected across points a and b, which have potential difference Vab = 12.0 V. a. What is the equivalent capacitance of the four capacitors? b. What is the charge on each of the four capacitors?arrow_forward
- A parallel-plate capacitor with an air gap has capacitance C0. It is connected to a battery with potential V0 that gives it charge Q0 and stored energy U0. After the capacitor is disconnected from the battery, a dielectric with constant = 3 is inserted into the air gap, completely filling it. In terms of the initial values, find the new capacitance C, charge Q, potential V, and stored energy U.arrow_forwardGiven the arrangement of capacitors in Figure P27.23, find an expression for the equivalent capacitance between points a and b. Figure P27.23 Problems 23 and 24.arrow_forwardConsider an infinitely long network with identical capacitors arranged as shown in Figure P27.82. Determine the equivalent capacitance of such a network. Each capacitor has a capacitance of 1.00 F.arrow_forward
- 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_forwardAn air-filled capacitor is made from two flat parallel plates 1.0 mm apart. The inside area of each plate is 8.0cm2. (a) What is the capacitance of this set of plates? (b) If the region between the plates is filled with a material whose dielectric constant is 6.0, what is the new capacitance?arrow_forwardReview One of the plates of a parallel-plate capacitor is suspended from the beam of a balance as shown in Figure P27.39. The distance d between the capacitor plates is 5.00 mm, and the cross-sectional area of the plates is 625 cm2. Determine the potential difference between the capacitor plates if a mass of 4.00 g is placed on the other pan of the balance to obtain static equilibrium. FIGURE P27.39arrow_forward
- Four capacitors are connected as shown in Figure P25.11. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking Vab = 15.0 V. Figure P25.11arrow_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_forwardWhat If? The two capacitors of Problem 13 (C1 = 5.00 F and C2 = 12.0 F) are now connected in series and to a 9.00-Y battery. Find (a) the equivalent capacitance of the combination. (b) the potential difference across each capacitor, and (c) the charge on each capacitor.arrow_forward
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- Principles 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 LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning