Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 17, Problem 15P
To determine

The work done in bringing a third charge from infinite to the point a given in the figure.

Expert Solution & Answer
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Answer to Problem 15P

The work done by the field is 1.80 μJ.

Explanation of Solution

The charges are +8.00nC, 8.00nCand +2.00nC  and the distances between the charges are given in the figure. Initially the third charge was at b and it is moved to the point c.

Physics, Chapter 17, Problem 15P

Write the expression for work done by the electric field

    Wfield=ΔU

Here, Wfield is the work done by the electric field,  ΔU is the change in potential energy

Substitute for ΔU in the above expression

  Wfield=UiUf                                                                                        (I)

Here, Uf is the final electric potential energy and Ui is the initial electric potential energy

Write the expression for initial electric potential energy for three charges

    Ui=k[q1q2r12+q2q3r23+q3q1r31]                                                                                (II)

Here, q1, q2,q3 are the three charges,  r12 is the initial distance between q1 and q2, r23 is the  initial distance between q2 and q3, r31 is the initial distance between q3 and q1 , Ui is the initial electric potential energy and k is a constant.

Write the expression for final electric potential energy for three charges

    Uf=k[q1q2r12+q2q3r23+q3q1r31]                                                                                (III)

Here, q1, q2,q3 are the three charges,  r12 is the final distance between q1 and q2, r23 is the  final distance between q2 and q3, r31 is the final distance between q3 and q1 , Uf is the final electric potential energy and k is a constant.

Substitute (II) and (III) in (I) to find Wfield

  Wfield=k[q1q2r12+q2q3r23+q3q1r31]k[q1q2r12+q2q3r23+q3q1r31]

Only the position of the third charge changes and hence the distance between the first two charges remains the same.

Substitute r12 for r12 in the above equation and solve further

  Wfield=k[q2q3(1r231r23)+q3q1(1r311r31)]                                                           (IV)

Substitute +8.00nC for q1,  8.00nC for q2,  +2.00nC for q3,  8.988×109Nm2C2 for k4.00cm for r23, 8.00cm for r31, 12.0cm for r23 and 12.0cm for r31 in (IV) to find Wfield

    Wfield=8.988×109Nm2C2[(8.00nC)(2.00nC)(14.00cm18.00cm)+(2.00nC)(8.00nC)(112.0cm112.0cm)]=8.988×109Nm2C2(8.00C)(2.00C)[(14.00m18.00m)+(112.0m112.0m)]×1018102=1.80×106 Nm=1.80 μJ

Thus, the work done by the electrical field is 1.80 μJ.

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Chapter 17 Solutions

Physics

Ch. 17.4 - Prob. 17.8PPCh. 17.5 - Prob. 17.5CPCh. 17.5 - Prob. 17.9PPCh. 17.6 - Prob. 17.6CPCh. 17.6 - Prob. 17.10PPCh. 17.6 - Prob. 17.11PPCh. 17.7 - Practice Problem 17.12 Charge and Stored Energy...Ch. 17 - Prob. 1CQCh. 17 - 2. Dry air breaks down for a voltage of about 3000...Ch. 17 - 3. A bird is perched on a high-voltage power line...Ch. 17 - 4. A positive charge is initially at rest in an...Ch. 17 - 5. Points A and B are at the same potential. What...Ch. 17 - Prob. 6CQCh. 17 - 7. Why are all parts of a conductor at the same...Ch. 17 - Prob. 8CQCh. 17 - Prob. 9CQCh. 17 - Prob. 11CQCh. 17 - Prob. 12CQCh. 17 - Prob. 13CQCh. 17 - Prob. 14CQCh. 17 - Prob. 15CQCh. 17 - Prob. 16CQCh. 17 - Prob. 17CQCh. 17 - Prob. 18CQCh. 17 - Prob. 19CQCh. 17 - Prob. 20CQCh. 17 - Prob. 21CQCh. 17 - Prob. 10CQCh. 17 - Prob. 1MCQCh. 17 - Prob. 2MCQCh. 17 - Prob. 3MCQCh. 17 - Prob. 4MCQCh. 17 - Prob. 5MCQCh. 17 - Prob. 6MCQCh. 17 - Prob. 7MCQCh. 17 - Prob. 8MCQCh. 17 - Prob. 9MCQCh. 17 - Prob. 10MCQCh. 17 - Prob. 11MCQCh. 17 - Prob. 12MCQCh. 17 - 1. In each of five situations, two point charges...Ch. 17 - 2. Two point charges, +5.0 μC and −2.0 μC, are...Ch. 17 - 3. A hydrogen atom has a single proton at its...Ch. 17 - 4. How much work is done by an applied force that...Ch. 17 - 5. The nucleus of a helium atom contains two...Ch. 17 - 6. Three point charges are located at the corners...Ch. 17 - Problems 7-10. Two point charges ( + 10.0 nC and −...Ch. 17 - Problems 7-10. Two point charges ( + 10.0 nC and −...Ch. 17 - Problems 7-10. Two point charges ( + 10.0 nC and −...Ch. 17 - Problems 7–10. Two point charges ( +10.0 nC and...Ch. 17 - 11. Find the electric potential energy for the...Ch. 17 - 12. In the diagram, how much work is done by the...Ch. 17 - 13. In the diagram, how much work is done by the...Ch. 17 - Prob. 14PCh. 17 - Prob. 15PCh. 17 - 16. A point charge q = + 3.0 nC moves through a...Ch. 17 - 17. An electron is moved from point A, where the...Ch. 17 - 18. Find the electric field and the potential at...Ch. 17 - Prob. 19PCh. 17 - 20. A charge of + 2.0 mC is located at x = 0, y =...Ch. 17 - 21. The electric potential at a distance of 20.0...Ch. 17 - 22. A spherical conductor with a radius of 75.0 cm...Ch. 17 - 23. A hollow metal sphere carries a charge of 6.0...Ch. 17 - 24. An array of four charges is arranged along the...Ch. 17 - 25. At a point P, a distance R0 from a positive...Ch. 17 - 26. Charges of + 2.0 nC and − 1.0 nC are located...Ch. 17 - Prob. 27PCh. 17 - 28. (a) Find the potential at points a and b in...Ch. 17 - 29. (a) In the diagram, what are the potentials at...Ch. 17 - 30. (a) In the diagram, what are the potentials at...Ch. 17 - Prob. 31PCh. 17 - 32. By rewriting each unit in terms of kilograms,...Ch. 17 - 33. Rank points A–E in order of the potential,...Ch. 17 - Prob. 34PCh. 17 - Prob. 35PCh. 17 - Prob. 36PCh. 17 - Prob. 37PCh. 17 - Prob. 38PCh. 17 - Prob. 39PCh. 17 - Prob. 40PCh. 17 - Prob. 41PCh. 17 - Prob. 43PCh. 17 - 43. A positive point charge is located at the...Ch. 17 - Prob. 44PCh. 17 - Prob. 45PCh. 17 - 46. Point P is at a potential of 500.0 kV, and...Ch. 17 - 47. An electron is accelerated from rest through a...Ch. 17 - 48. As an electron moves through a region of...Ch. 17 - Prob. 49PCh. 17 - 50. An electron beam is deflected upward through...Ch. 17 - 51. In the electron gun of Example 17.8, if the...Ch. 17 - 52. In the electron gun of Example 17.8, if the...Ch. 17 - 53. An electron (charge −e) is projected...Ch. 17 - 54. An alpha particle (charge +2e) moves through a...Ch. 17 - 55. In 1911, Ernest Rutherford discovered the...Ch. 17 - 56. The figure shows a graph of electric potential...Ch. 17 - 57. Repeat Problem 56 for an electron rather than...Ch. 17 - 58. A 2.0 μE capacitor is connected to a 9.0 V...Ch. 17 - 59. The plates of a 15.0 μE capacitor have net...Ch. 17 - 60. If a capacitor has a capacitance of 10.2 μE...Ch. 17 - 61. A parallel plate capacitor has a capacitance...Ch. 17 - 62. A parallel plate capacitor has plates of area...Ch. 17 - 63. A parallel plate capacitor has plates of area...Ch. 17 - Prob. 64PCh. 17 - Prob. 65PCh. 17 - Prob. 66PCh. 17 - Prob. 67PCh. 17 - Prob. 68PCh. 17 - Prob. 69PCh. 17 - Prob. 70PCh. 17 - Prob. 71PCh. 17 - Prob. 72PCh. 17 - Prob. 73PCh. 17 - Prob. 74PCh. 17 - Prob. 75PCh. 17 - Prob. 76PCh. 17 - Prob. 77PCh. 17 - 78. What is the maximum electric energy density...Ch. 17 - Prob. 79PCh. 17 - Prob. 80PCh. 17 - Prob. 81PCh. 17 - Prob. 82PCh. 17 - Prob. 83PCh. 17 - 84. A parallel plate capacitor is composed of two...Ch. 17 - Prob. 85PCh. 17 - 86. A parallel plate capacitor has a charge of...Ch. 17 - Prob. 87PCh. 17 - Prob. 88PCh. 17 - Prob. 89PCh. 17 - Prob. 90PCh. 17 - Prob. 91PCh. 17 - Prob. 92PCh. 17 - Prob. 93PCh. 17 - Prob. 94PCh. 17 - Prob. 95PCh. 17 - Prob. 96PCh. 17 - Prob. 97PCh. 17 - Prob. 98PCh. 17 - Prob. 99PCh. 17 - Prob. 100PCh. 17 - Prob. 101PCh. 17 - Prob. 102PCh. 17 - Prob. 103PCh. 17 - Prob. 104PCh. 17 - Prob. 105PCh. 17 - 106. ✦ The potential difference across a cell...Ch. 17 - Prob. 107PCh. 17 - Prob. 108PCh. 17 - Prob. 109PCh. 17 - Prob. 110PCh. 17 - Prob. 111PCh. 17 - Prob. 112PCh. 17 - Prob. 113PCh. 17 - Prob. 114PCh. 17 - Prob. 115PCh. 17 - Prob. 116PCh. 17 - Prob. 117PCh. 17 - Prob. 118PCh. 17 - Prob. 119PCh. 17 - Prob. 120PCh. 17 - Prob. 121PCh. 17 - Prob. 122PCh. 17 - Prob. 123PCh. 17 - Prob. 124PCh. 17 - An air ionizer fillers particles of dust, pollen,...Ch. 17 - Prob. 126PCh. 17 - Prob. 127PCh. 17 - Prob. 128PCh. 17 - Prob. 129P
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