Physics for Scientists and Engineers with Modern Physics
4th Edition
ISBN: 9780131495081
Author: Douglas C. Giancoli
Publisher: Addison-Wesley
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Textbook Question
Chapter 24, Problem 61P
(II) Repeat Problem 60 (Fig. 24–31) but assume the separation d1 ≠ d2.
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Sketch the harmonic on graphing paper.
Exercise 1:
(a) Using the explicit formulae derived in the lectures for the (2j+1) × (2j + 1) repre-
sentation matrices Dm'm, (J/h), derive the 3 × 3 matrices corresponding to the case
j = 1.
(b) Verify that they satisfy the so(3) Lie algebra commutation relation:
[D(Î₁/ħ), D(Î₂/h)]m'm₁ = iƊm'm² (Ĵ3/h).
(c) Prove the identity
3
Dm'm,(β) = Σ (D(Ρ)D(Ρ))m'¡m; ·
i=1
Sketch the harmonic.
Chapter 24 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 24.1 - Graphs for charge versus voltage are shown in Fig....Ch. 24.2 - Two circular plates of radius 5.0 cm are separated...Ch. 24.2 - What is the capacitance per unit length of a...Ch. 24.3 - Consider two identical capacitors C1 = C2 = 10 F....Ch. 24.5 - Return to the Chapter-Opening Question, page 628,...Ch. 24 - Suppose two nearby conductors carry the same...Ch. 24 - Suppose the separation of plates d in a...Ch. 24 - Suppose one of the plates of a parallel-plate...Ch. 24 - When a battery is connected to a capacitor, why do...Ch. 24 - Describe a sample method of measuring 0 using a...
Ch. 24 - Suppose three identical capacitors are connected...Ch. 24 - A large copper sheet of thickness is placed...Ch. 24 - The parallel plates of an isolated capacitor carry...Ch. 24 - How does the energy in a capacitor change if (a)...Ch. 24 - If the voltage across a capacitor is doubled, the...Ch. 24 - An isolated charged capacitor has horizontal...Ch. 24 - Suppose a battery remains connected to the...Ch. 24 - How does the energy stored in a capacitor change...Ch. 24 - For dielectrics consisting of polar molecules, how...Ch. 24 - A dielectric is pulled out from between the plates...Ch. 24 - We have seen that the capacitance C depends on the...Ch. 24 - What value might we assign to the dielectric...Ch. 24 - (I) The two plates of a capacitor hold +2800 C and...Ch. 24 - (I) How much charge flows from a 12.0-V battery...Ch. 24 - (I) The potential difference between two short...Ch. 24 - (I) The charge on a capacitor increases by 26 C...Ch. 24 - (II) A 7.7-F capacitor is charged by a 125-V...Ch. 24 - (II) An isolated capacitor C1 carries a charge Q0....Ch. 24 - (II) It takes 15 J of energy to move a 0.20-mC...Ch. 24 - (II) A 2.70-F capacitor is charged to 475 V and a...Ch. 24 - (II) Compact ultracapacitors with capacitance...Ch. 24 - (II) In a dynamic random access memory (DRAM)...Ch. 24 - (I) To make a 0.40-F capacitor, what area must the...Ch. 24 - (I) What is the capacitance per unit length (F/m)...Ch. 24 - (I) Determine the capacitance of the Earth,...Ch. 24 - (II) Use Gausss law to show that E=0 inside the...Ch. 24 - (II) Dry air will break down if the electric field...Ch. 24 - (II) An electric field of 4.80 105V/m is desired...Ch. 24 - (II) How strong is the electric field between the...Ch. 24 - (II) A large metal sheet of thickness is placed...Ch. 24 - (III) Small distances are commonly measured...Ch. 24 - (III) In an electrostatic air cleaner...Ch. 24 - (I) The capacitance of a portion of a circuit is...Ch. 24 - (I) (a) Six 3.8-F capacitors are connected in...Ch. 24 - (II) Given three capacitors, C1 = 2.0 F, C2 = 1.5...Ch. 24 - (II) Suppose three parallel-plate capacitors,...Ch. 24 - (II) An electric circuit was accidentally...Ch. 24 - (II) Three conducting plates, each of area A, are...Ch. 24 - (II) Consider three capacitors, of capacitance...Ch. 24 - (II) A 0.50-F and a 0.80-F capacitor are connected...Ch. 24 - (II) In Fig. 2423, suppose C1 = C2 = C3 = C4 = C....Ch. 24 - (II) Suppose in Fig. 2423 that C1 = C2 = C3 = 16.0...Ch. 24 - (II) The switch S in Mg. 2424 is connected...Ch. 24 - (II) (a) Determine the equivalent capacitance...Ch. 24 - FIGURE 2425 Problems 32 and 33. (II) Suppose in...Ch. 24 - (II) Two capacitors connected in parallel produce...Ch. 24 - (II) In the capacitance bridge shown m Fig. 2426,...Ch. 24 - (II) Two capacitors, C1 = 3200 pF and C2 = 1800...Ch. 24 - (II) (a) Determine the equivalent capacitance of...Ch. 24 - (II) In Fig. 2427, let C1 = 2.00 F, C2 = 3.00 F,...Ch. 24 - (III) Suppose one plate of a parallel-plate...Ch. 24 - (III) A voltage V is applied to the capacitor...Ch. 24 - (I) 2200 V is applied to a 2800-pF capacitor. How...Ch. 24 - (I) There is an electric field near the Earths...Ch. 24 - (I) How much energy is stored by the electric...Ch. 24 - (II) A parallel-plate capacitor has fixed charges...Ch. 24 - (II) In Fig. 2427, Let V = 10.0 V and C1 = C2 = C3...Ch. 24 - (II) How much energy must a 28-V battery expend to...Ch. 24 - (II) (a) Suppose the outer radius Ra of a...Ch. 24 - (II) A 2.2-F capacitor is charged by a 12.0-V...Ch. 24 - (II) How much work would be required to remove a...Ch. 24 - (II) (a) Show that each plate of a parallel-plate...Ch. 24 - (II) Show that the electrostatic energy stored in...Ch. 24 - (II) When two capacitors are connected in parallel...Ch. 24 - (II) For commonly used CMOS (complementary metal...Ch. 24 - (I) What is the capacitance of two square parallel...Ch. 24 - (II) Suppose the capacitor in Example 2411 remains...Ch. 24 - (II) How much energy would be stored in the...Ch. 24 - (II) In the DRAM computer chip of Problem 10, the...Ch. 24 - (II) A 3500-pF air-gap capacitor is connected to a...Ch. 24 - (II) Two different dielectrics each fill half the...Ch. 24 - (II) Two different dielectrics fill the space...Ch. 24 - (II) Repeat Problem 60 (Fig. 2431) but assume the...Ch. 24 - (II) Two identical capacitors are connected in...Ch. 24 - (III) A slab of width d and dielectric constant K...Ch. 24 - (III) The quantity of liquid (such as cryogenic...Ch. 24 - (II) Show that the capacitor in Example 2412 with...Ch. 24 - (II) Repeat Example 24-12 assuming the battery...Ch. 24 - (II) Using Example 2412 as a model, derive a...Ch. 24 - (II) In Example 2412 what percent of the stored...Ch. 24 - (III) The capacitor shown in Fig. 2434 is...Ch. 24 - (a) A general rule for estimating the capacitance...Ch. 24 - A cardiac defibrillator is used to shock a heart...Ch. 24 - A homemade capacitor is assembled by placing two...Ch. 24 - An uncharged capacitor is connected to a 34.0-V...Ch. 24 - It takes 18.5 J of energy to move a 13.0-mC charge...Ch. 24 - A huge 3.0-F capacitor has enough stored energy to...Ch. 24 - A coaxial cable, Fig. 2435, consists of an inner...Ch. 24 - The electric field between the plates of a...Ch. 24 - Capacitors can be used as electric charge...Ch. 24 - A parallel-plate capacitor is isolated with a...Ch. 24 - In lightning storms, the potential difference...Ch. 24 - A multilayer film capacitor has a maximum voltage...Ch. 24 - A 3.5 F capacitor is charged by a 12.4-V battery...Ch. 24 - The power supply for a pulsed nitrogen laser has a...Ch. 24 - A parallel-plate capacitor has square plates 12 cm...Ch. 24 - The variable capacitance of an old radio tuner...Ch. 24 - A high-voltage supply can be constructed from a...Ch. 24 - A 175-pF capacitor is connected in series with an...Ch. 24 - A parallel-plate capacitor with plate area 2.0 cm2...Ch. 24 - In the circuit shown in Fig. 2437. C1 = 1.0 F, C2...Ch. 24 - The long cylindrical capacitor shown in Fig. 2438...Ch. 24 - A parallel-plate capacitor has plate area A, plate...Ch. 24 - Consider the use of capacitors as memory cells. A...Ch. 24 - To get an idea how big a farad is, suppose you...Ch. 24 - A student wearing shoes with thin insulating soles...Ch. 24 - A parallel-plate capacitor with plate area A = 2.0...Ch. 24 - Let us try to estimate the maximum static...Ch. 24 - Paper has a dielectric constant K = 3.7 and a...Ch. 24 - (II) Six physics students were each given an air...
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