Domanda del libro di testo
A 100 A current circulates around a 2.0-mm-diameter superconducting ring. What is the ring's magnetic dipole moment?
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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 17b
The on-axis magnetic field strength 10 cm from a small bar magnet is 500 μT. What is the on-axis field strength 15 cm from the magnet?
Guida verificata passo dopo passo1
Step 1: Understand the relationship between the magnetic field strength and distance from the magnet. For a small bar magnet, the magnetic field strength on the axis decreases approximately as the cube of the distance from the magnet. This means the field strength is proportional to 1/(distance³).
Step 2: Write the formula for the magnetic field strength at a distance from the magnet: \( B \propto \frac{1}{r^3} \), where \( B \) is the magnetic field strength and \( r \) is the distance from the magnet.
Step 3: Set up the ratio of the magnetic field strengths at two distances using the proportionality: \( \frac{B_2}{B_1} = \left( \frac{r_1}{r_2} \right)^3 \), where \( B_1 \) and \( B_2 \) are the field strengths at distances \( r_1 \) and \( r_2 \), respectively.
Step 4: Substitute the given values into the ratio formula. Here, \( B_1 = 500 \, \mu T \), \( r_1 = 10 \, \text{cm} \), and \( r_2 = 15 \, \text{cm} \). The equation becomes \( B_2 = B_1 \cdot \left( \frac{r_1}{r_2} \right)^3 \).
Step 5: Simplify the expression to find \( B_2 \). Perform the cube of the ratio \( \left( \frac{10}{15} \right)^3 \) and multiply it by \( B_1 \). This will give the magnetic field strength at 15 cm from the magnet.
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Concetti chiave
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Magnetic Field Strength
Magnetic field strength, often denoted as B, is a measure of the magnetic force experienced by a unit magnetic pole in a magnetic field. It is typically measured in teslas (T) or microteslas (μT). The strength of the magnetic field decreases with distance from the magnet, following specific mathematical relationships depending on the type of magnet.
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Percorso guidato
05:30
Magnetic Fields and Magnetic Dipoles
Inverse Square Law
The inverse square law states that the strength of a physical quantity (like gravitational or magnetic fields) decreases with the square of the distance from the source. For magnetic fields produced by dipoles, the field strength decreases as the distance increases, specifically following a 1/r^3 relationship for a bar magnet along its axis, where r is the distance from the magnet.
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Percorso guidato
05:26The Inverse-Square Law for Intensity
Bar Magnet Characteristics
A bar magnet has a north and south pole, creating a magnetic field that emanates from the north pole and returns to the south pole. The field strength is strongest at the poles and diminishes with distance. Understanding the geometry and field lines of a bar magnet is crucial for predicting how the magnetic field behaves at various distances.
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Percorso guidato
05:30Magnetic Fields and Magnetic Dipoles
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A 100 A current circulates around a 2.0-mm-diameter superconducting ring. What is the on-axis magnetic field strength 5.0 cm from the ring?
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