Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 19, Problem 79P

(a)

To determine

The magnitude and direction of the magnetic field due to wire 1 at the location of wire 2.

(a)

Expert Solution
Check Mark

Answer to Problem 79P

The magnetic field due to wire 1 at the location of wire 2 is B1=μ0I12πd to the plane of wires_.

Explanation of Solution

Given that the separation between wires is d, and the length of wires is L.

The direction of the magnetic field produced by wire 1 can be determined by the right-hand rule 2. By placing the thumb along the current I1, the curled fingers shows the direction of the magnetic field as shown in Figure 1.

Physics, Chapter 19, Problem 79P

Write the expression for the magnitude of magnetic field at a distance r from a current carrying wire.

B=μ0I2πr (I)

Here, B is the magnetic field, μ0 is the permeability of free space, I is the current, and r is the distance.

Conclusion:

From Figure 1, the use of right-hand rule 2 results, the direction of magnetic field due to wire 1 at the location of wire 2 perpendicular to the plane of the wires.

Apply the equation (I) to the given system to obtain the expression for the magnitude of the magnetic field due to wire 1 at the location of wire 2.

B1=μ0I12πd

Write the magnetic field due to wire 1 at the location of wire 2 including magnitude and direction.

B1=μ0I12πd to the plane of wires

Therefore, the magnetic field due to wire 1 at the location of wire 2 is B1=μ0I12πd to the plane of wires_.

(b)

To determine

The magnitude and direction of the magnetic force on wire 2.

(b)

Expert Solution
Check Mark

Answer to Problem 79P

The magnetic force on wire 2 is F=μ0I1I2L2πdtoward I1_.

Explanation of Solution

Given that the separation between wires is d, and the length of wires is L.

The direction of the magnetic force on wire 2 can be determined by the right-hand rule 2 as shown in Figure 1.

Write the expression for the magnetic force due to a current carrying wire.

F=IL×B (II)

Here, F is the magnetic force, I is the current, L is the length if the wire, and B is the magnetic field.

Conclusion:

From Figure 1, the use of right-hand rule 2 results, the direction of magnetic force on wire 2 towards the current I1.

Apply the equation (II) to the given system to obtain the expression for the magnetic force on wire 2.

F=I2L×B1=I2LB1toward I1 (III)

Use expression for B1 in (III).

F=I2L(μ0I12πd)toward I1=μ0I1I2L2πdtoward I1

Therefore, the magnetic force on wire 2 is F=μ0I1I2L2πdtoward I1_.

(c)

To determine

The magnitude and direction of the magnetic field due to wire 2 at the location of wire 1.

(c)

Expert Solution
Check Mark

Answer to Problem 79P

The magnetic field due to wire 2 at the location of wire 1 is B2=μ0I22πd to the plane of wires and opposite to B1_.

Explanation of Solution

Given that the separation between wires is d, and the length of wires is L.

The direction of the magnetic field produced by wire 2 can be determined by the right-hand rule 2. By placing the thumb along the current I2, the curled fingers shows the direction of the magnetic field. The process is similar as done in part (a).

Equation (I) gives expression for the magnitude of magnetic field at a distance r from a current carrying wire.

B=μ0I2πr

Conclusion:

The use of right-hand rule 2 results, the direction of magnetic field due to wire 2 at the location of wire 1 perpendicular to the plane of the wires and opposite to B1.

Apply the equation (I) to the given system to obtain the expression for the magnitude of the magnetic field due to wire 2 at the location of wire 1.

B2=μ0I22πd

Write the magnetic field due to wire 2 at the location of wire 1 including magnitude and direction.

B2=μ0I22πd to the plane of wires and opposite to B1

Therefore, the magnetic field due to wire 2 at the location of wire 1 is B2=μ0I22πd to the plane of wires and opposite to B1_.

(d)

To determine

The magnitude and direction of the magnetic force on wire 1.

(d)

Expert Solution
Check Mark

Answer to Problem 79P

The magnetic force on wire 1 is F=μ0I1I2L2πdtoward I2_.

Explanation of Solution

Given that the separation between wires is d, and the length of wires is L.

The direction of the magnetic force on wire 1 can be determined by the right-hand rule 2 similar as done in part (b).

Equation (II) gives the expression for the magnetic force due to a current carrying wire.

F=IL×B

Conclusion:

The use of right-hand rule 2 results, the direction of magnetic force on wire 1 towards the current I2.

Apply the equation (II) to the given system to obtain the expression for the magnetic force on wire 1.

F=I1L×B2=I1LB1toward I2 (III)

Use expression for B2 in (III).

F=I1L(μ0I22πd)toward I2=μ0I1I2L2πdtoward I2

Therefore, the magnetic force on wire 1 is F=μ0I1I2L2πdtoward I2_.

(e)

To determine

Whether the parallel currents in the same direction attract or repel, and whether the parallel currents in opposite direction attract or repel.

(e)

Expert Solution
Check Mark

Answer to Problem 79P

The parallel currents in the same direction attract_, and the parallel currents in opposite direction repel_.

Explanation of Solution

The magnetic force is determined from the cross product of the length (along the current direction) and the magnetic field. If the currents in the parallel wires are in the same direction, the forces will be attractive in nature.

Reversing the current’s direction causes the cross products to be oppositely directed. This causes the force on each wire is away from the other wire. Thus, antiparallel currents repels.

Conclusion:

Therefore, the parallel currents in the same direction attract_, and the parallel currents in opposite direction repel_.

(f)

To determine

Whether the magnitudes and directions of the magnetic force due to the current carrying wires are consistent with Newton’s third law.

(f)

Expert Solution
Check Mark

Answer to Problem 79P

The magnitudes and directions of the magnetic force due to the current carrying wires are consistent with Newton’s third law.

Explanation of Solution

The forces on the two currents are equal in magnitude and opposite in direction. According to Newton’s third law, for every action there is an equal and opposite reaction. In the case of current passing through the parallel wires, the forces can be identified as one opposes the other but equal in magnitude.

Both the parallel currents and antiparallel currents are consistent with Newton’s third law, since the forces on the two currents are equal and opposite in direction.

Conclusion:

Therefore, the magnitudes and directions of the magnetic force due to the current carrying wires are consistent with Newton’s third law.

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Chapter 19 Solutions

Physics

Ch. 19.6 - 19.6 Suppose the magnetic field in Fig. 19.28 were...Ch. 19.6 - 19.8 Magnetic Force on a Current-Carrying Wire A...Ch. 19.7 - CHECKPOINT 19.7 Suppose the coil of wire in Fig....Ch. 19.7 - Practice Problem 19.9 Torque on a Coil Starting...Ch. 19.8 - 19.8 What is the direction of the magnetic field...Ch. 19.8 - 19.10 Field Midway Between Two Wires Find the...Ch. 19.9 - Prob. 19.11PPCh. 19 - Prob. 1CQCh. 19 - Prob. 2CQCh. 19 - Prob. 3CQCh. 19 - Prob. 4CQCh. 19 - Prob. 5CQCh. 19 - Prob. 6CQCh. 19 - Prob. 7CQCh. 19 - Prob. 8CQCh. 19 - Prob. 9CQCh. 19 - Prob. 10CQCh. 19 - Prob. 11CQCh. 19 - Prob. 12CQCh. 19 - Prob. 13CQCh. 19 - Prob. 14CQCh. 19 - Prob. 15CQCh. 19 - Prob. 16CQCh. 19 - Prob. 17CQCh. 19 - Prob. 18CQCh. 19 - Prob. 19CQCh. 19 - Prob. 20CQCh. 19 - Prob. 21CQCh. 19 - Prob. 22CQCh. 19 - Prob. 23CQCh. 19 - Prob. 1MCQCh. 19 - Prob. 2MCQCh. 19 - Multiple-Choice Questions 1-4. In the figure, four...Ch. 19 - Prob. 4MCQCh. 19 - Prob. 5MCQCh. 19 - Prob. 6MCQCh. 19 - Prob. 7MCQCh. 19 - Prob. 8MCQCh. 19 - Multiple-Choice Questions 6-9. A wire carries...Ch. 19 - Prob. 10MCQCh. 19 - 11. The magnetic forces that two parallel wires...Ch. 19 - Prob. 12MCQCh. 19 - 1. At which point in the diagram is the magnetic...Ch. 19 - 2. Draw vector arrows to indicate the direction...Ch. 19 - Problems 3-6. Sketch some magnetic field lines for...Ch. 19 - Prob. 4PCh. 19 - Prob. 5PCh. 19 - Problems 3–6. Sketch some magnetic field lines for...Ch. 19 - 7. Find the magnetic force exerted on an electron...Ch. 19 - 8. Find the magnetic force exerted on a proton...Ch. 19 - 9. A uniform magnetic field points north; its...Ch. 19 - 10. A uniform magnetic field points vertically...Ch. 19 - Problems 11-14. Several electrons move at speed...Ch. 19 - 12. Find the magnetic force on the electron at...Ch. 19 - 12. Find the magnetic force on the electron at...Ch. 19 - Problems 11-14. Several electrons move at speed...Ch. 19 - 15. A magnet produces a 0.30 T field between its...Ch. 19 - 16. At a certain point on Earth’s surface in the...Ch. 19 - 17. A cosmic ray muon with the same charge as an...Ch. 19 - 18. In a CRT. electrons moving at 1.8 × 107 m/s...Ch. 19 - 19. A positron (q = +e) moves at 5.0 × 107 m/s in...Ch. 19 - 20. ✦ An electron moves with speed 2.0 × 105 m/s...Ch. 19 - 21. ✦ An electron moves with speed 2.0 × 105 m/s...Ch. 19 - 19.3 Charged Particle Moving Perpendicularly to a...Ch. 19 - 23. Six protons move (at speed v) in magnetic...Ch. 19 - 24. An electron moves at speed 8.0 × 105 m/s in a...Ch. 19 - 25. The magnetic field in a hospital’s cyclotron...Ch. 19 - 26. The magnetic field in a cyclotron used in...Ch. 19 - 27. The magnetic field in a cyclotron used to...Ch. 19 - 28. A beam of α particles (helium nuclei) is used...Ch. 19 - 29. A singly charged ion of unknown mass moves in...Ch. 19 - 30. In one type of mass spectrometer, ions having...Ch. 19 - 31. Natural carbon consists of two different...Ch. 19 - 32. After being accelerated through a potential...Ch. 19 - 33. A sample containing carbon (atomic mass 12 u),...Ch. 19 - Prob. 34PCh. 19 - 35. Show that the time for one revolution of a...Ch. 19 - 36. Crossed electric and magnetic fields are...Ch. 19 - 37. A current I = 40.0 A flows through a strip of...Ch. 19 - 38. In Problem 37, if the width of the strip is...Ch. 19 - 39. In Problem 37, the width of the strip is 3.5...Ch. 19 - 40. The strip in the diagram is used as a Hall...Ch. 19 - 41. A strip of copper 2.0 cm wide carries a...Ch. 19 - Prob. 42PCh. 19 - 43. An electromagnetic flowmeter is used to...Ch. 19 - 44. A charged particle is accelerated from rest...Ch. 19 - 45. A straight wire segment of length 0.60 m...Ch. 19 - 46. A straight wire segment of length 25 cm...Ch. 19 - 47. Parallel conducting tracks, separated by 2.0...Ch. 19 - 48. An electromagnetic rail gun can fire a...Ch. 19 - 49. A straight, stiff wire of length 1.00 m and...Ch. 19 - Prob. 50PCh. 19 - Prob. 51PCh. 19 - Prob. 52PCh. 19 - 53. ✦ A straight wire is aligned east-west in a...Ch. 19 - 54. A straight wire is aligned north-south in a...Ch. 19 - 55. In each of six electric motors, a cylindrical...Ch. 19 - 56. In an electric motor, a circular coil with...Ch. 19 - 57. In an electric motor, a coil with 100 turns of...Ch. 19 - 58. A square loop of wire of side 3.0 cm carries...Ch. 19 - 59. The intrinsic magnetic dipole moment of the...Ch. 19 - 60. In a simple model, the electron in a hydrogen...Ch. 19 - 61. A certain fixed length L of wire carries a...Ch. 19 - 62. Use the following method to show that the...Ch. 19 - 63. A square loop of wire with side 0.60 m carries...Ch. 19 - Prob. 64PCh. 19 - 65. Estimate the magnetic field at distances of...Ch. 19 - Prob. 66PCh. 19 - 67. Kieran measures the magnetic field of an...Ch. 19 - 68. Two wires each carry 10.0 A of current (in...Ch. 19 - In Problem 67, what is the magnetic field at a...Ch. 19 - What is the magnetic field at point P if the...Ch. 19 - 70. Point P is midway between two long, straight,...Ch. 19 - 70. Point P is midway between two long, straight,...Ch. 19 - Prob. 72PCh. 19 - Prob. 73PCh. 19 - 74. Two long straight wires carry the same amount...Ch. 19 - 75. In Problem 74, find the magnetic field at...Ch. 19 - 76. In Problem 74, find the magnetic field at...Ch. 19 - 77. A solenoid of length 0.256 m and radius 2.0 cm...Ch. 19 - 78. Two long straight parallel wires separated by...Ch. 19 - Prob. 79PCh. 19 - Two concentric circular wire loops in the same...Ch. 19 - 81. You are designing the main solenoid for an MRI...Ch. 19 - 82. A solenoid has 4850 turns per meter and radius...Ch. 19 - 83. Find the magnetic field at the center of the...Ch. 19 - 84. Find the magnetic field at point P, the...Ch. 19 - Prob. 85PCh. 19 - Prob. 86PCh. 19 - Prob. 87PCh. 19 - 88. A number of wires carry currents into or out...Ch. 19 - 89. ✦ An infinitely long, thick cylindrical shell...Ch. 19 - 90. In this problem, use Ampère’s law to show...Ch. 19 - Prob. 91PCh. 19 - Prob. 92PCh. 19 - Prob. 93PCh. 19 - Prob. 94PCh. 19 - Prob. 95PCh. 19 - Prob. 96PCh. 19 - Prob. 97PCh. 19 - Prob. 98PCh. 19 - Prob. 99PCh. 19 - Prob. 100PCh. 19 - Prob. 101PCh. 19 - Prob. 102PCh. 19 - Prob. 103PCh. 19 - Prob. 104PCh. 19 - Prob. 105PCh. 19 - 106. Two conducting wires perpendicular to the...Ch. 19 - Prob. 107PCh. 19 - Prob. 108PCh. 19 - 110. A solenoid with 8500 turns per meter has...Ch. 19 - Prob. 109PCh. 19 - Prob. 111PCh. 19 - Prob. 115PCh. 19 - Prob. 112PCh. 19 - Prob. 113PCh. 19 - Prob. 114PCh. 19 - Prob. 117PCh. 19 - Prob. 116PCh. 19 - Prob. 118PCh. 19 - Prob. 120PCh. 19 - Prob. 121PCh. 19 - Prob. 122PCh. 19 - Prob. 123PCh. 19 - Prob. 124PCh. 19 - Prob. 125PCh. 19 - Prob. 126PCh. 19 - Prob. 127PCh. 19 - Prob. 128P
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