Domanda del libro di testo
What is the magnetic field at the position of the dot in FIGURE EX29.6? Give your answer as a vector.
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Ch 29: The Magnetic Field
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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TOC.tableOfContents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Capitolo 29, Problema 3
A proton moves along the x-axis with vₓ = 1.0 x 10⁷ m/s. As it passes the origin, what are the strength and direction of the magnetic field at the (x, y, z) positions (a) (1 cm, 0 cm, 0 cm), (b) (0 cm, 1 cm, 0 cm), and (c) (0 cm, -2 cm, 0 cm)?
Guida verificata passo dopo passo1
Step 1: Recall the formula for the magnetic field produced by a moving charge. The magnetic field at a point due to a moving charge is given by **B = (μ₀ / 4π) * (q * v × r̂) / r²**, where μ₀ is the permeability of free space, q is the charge, v is the velocity vector, r̂ is the unit vector pointing from the charge to the observation point, and r is the distance between the charge and the observation point.
Step 2: Identify the given values. The charge of a proton is q = 1.6 × 10⁻¹⁹ C, the velocity vector is **v = (1.0 × 10⁷ m/s) î**, and the observation points are (a) (1 cm, 0 cm, 0 cm), (b) (0 cm, 1 cm, 0 cm), and (c) (0 cm, -2 cm, 0 cm). Convert the distances to meters: 1 cm = 0.01 m, 2 cm = 0.02 m.
Step 3: For each observation point, calculate the distance vector **r** and the unit vector **r̂**. For example, for point (a), **r = (0.01 m) î**, and **r̂ = r / |r| = î**. Similarly, calculate **r** and **r̂** for points (b) and (c).
Step 4: Compute the cross product **v × r̂** for each observation point. For point (a), since **v** and **r̂** are parallel, the cross product is zero, meaning the magnetic field at (1 cm, 0 cm, 0 cm) is zero. For points (b) and (c), use the right-hand rule to determine the direction of **v × r̂** and calculate its magnitude.
Step 5: Substitute the values into the formula for **B** to find the magnitude and direction of the magnetic field at each point. Use the calculated **v × r̂**, the distance **r**, and the constants μ₀ = 4π × 10⁻⁷ T·m/A and q = 1.6 × 10⁻¹⁹ C to determine the magnetic field strength at points (b) and (c).
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Magnetic Field Due to a Moving Charge
A moving charge, such as a proton, generates a magnetic field around it. The strength and direction of this magnetic field can be determined using the right-hand rule and the Biot-Savart law, which relates the magnetic field to the velocity of the charge and its distance from the point of interest.
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Percorso guidato
10:47
Magnetic Field Produced by Moving Charges
Right-Hand Rule
The right-hand rule is a mnemonic used to determine the direction of the magnetic field produced by a moving charge. By pointing the thumb of the right hand in the direction of the charge's velocity and curling the fingers, the direction of the magnetic field lines can be found, which are perpendicular to both the velocity and the direction of the magnetic field.
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19:11Force on Moving Charges & Right Hand Rule
Coordinate System and Position Vectors
In physics, a coordinate system is used to define the position of points in space. The positions given in the question (e.g., (1 cm, 0 cm, 0 cm)) represent points in a three-dimensional Cartesian coordinate system, where the x, y, and z coordinates indicate the location in space relative to the origin. Understanding this system is crucial for calculating the magnetic field at specific points.
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Percorso guidato
07:07Final Position Vector
Pratica correlata
Domanda del libro di testo
What are the magnetic fields at points a to c in FIGURE EX29.13? Give your answers as vectors.
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Domanda del libro di testo
The element niobium, which is a metal, is a superconductor (i.e., no electrical resistance) at temperatures below 9 K. However, the superconductivity is destroyed if the magnetic field at the surface of the metal reaches or exceeds 0.10 T. What is the maximum current in a straight, 3.0-mm-diameter superconducting niobium wire?
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