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QUESTION 8 You want to produce a magnetic field of magnitude 2.26E-5 T at a distance of 4.05E-2 m from a long, straight wire's center. What current is required to produce this field (in Amp)? Permeability of vacuum: 0= 1.26E-6 T-m/A

QUESTION 8 You want to produce a magnetic field of magnitude 2.26E-5 T at a distance of 4.05E-2 m from a long, straight wire's center. What current is required to produce this field (in Amp)? Permeability of vacuum: 0= 1.26E-6 T-m/A

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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### Physics Question 8: Calculating Current for Magnetic Field Production **Problem Statement:** You want to produce a magnetic field of magnitude \( 2.26 \times 10^{-5} \) T at a distance of \( 4.05 \times 10^{-2} \) m from a long, straight wire's center. What current is required to produce this field (in Amperes)? **Given Parameters:** - Magnetic Field (\( B \)): \( 2.26 \times 10^{-5} \) Tesla - Distance from Wire (\( r \)): \( 4.05 \times 10^{-2} \) meters - Permeability of Vacuum (\( \mu_0 \)): \( 1.26 \times 10^{-6} \) T·m/A ### Solution: *Detailed explanation of the calculations required to determine the current necessary to generate the specified magnetic field.* 1. **Formula Used:** The magnetic field \( B \) around a long, straight conductor carrying current \( I \) is given by the Ampère's Law formula: \[ B = \frac{\mu_0 I}{2\pi r} \] 2. **Rearrange the Formula to Solve for Current \( I \):** \[ I = \frac{B \cdot 2\pi r}{\mu_0} \] 3. **Substitute the Known Values:** \[ I = \frac{2.26 \times 10^{-5} \, \text{T} \cdot 2\pi \cdot 4.05 \times 10^{-2} \, \text{m}}{1.26 \times 10^{-6} \, \text{T·m/A}} \] 4. **Calculate \( I \):** \[ I = \frac{2.26 \times 10^{-5} \cdot 2\pi \cdot 4.05 \times 10^{-2}}{1.26 \times 10^{-6}} \] \[ I = \frac{2.26 \cdot 2 \cdot 3.14159 \cdot 0.0405}{1.26 \times 10^{-6}} \] \[ I
Transcribed Image Text:### Physics Question 8: Calculating Current for Magnetic Field Production **Problem Statement:** You want to produce a magnetic field of magnitude \( 2.26 \times 10^{-5} \) T at a distance of \( 4.05 \times 10^{-2} \) m from a long, straight wire's center. What current is required to produce this field (in Amperes)? **Given Parameters:** - Magnetic Field (\( B \)): \( 2.26 \times 10^{-5} \) Tesla - Distance from Wire (\( r \)): \( 4.05 \times 10^{-2} \) meters - Permeability of Vacuum (\( \mu_0 \)): \( 1.26 \times 10^{-6} \) T·m/A ### Solution: *Detailed explanation of the calculations required to determine the current necessary to generate the specified magnetic field.* 1. **Formula Used:** The magnetic field \( B \) around a long, straight conductor carrying current \( I \) is given by the Ampère's Law formula: \[ B = \frac{\mu_0 I}{2\pi r} \] 2. **Rearrange the Formula to Solve for Current \( I \):** \[ I = \frac{B \cdot 2\pi r}{\mu_0} \] 3. **Substitute the Known Values:** \[ I = \frac{2.26 \times 10^{-5} \, \text{T} \cdot 2\pi \cdot 4.05 \times 10^{-2} \, \text{m}}{1.26 \times 10^{-6} \, \text{T·m/A}} \] 4. **Calculate \( I \):** \[ I = \frac{2.26 \times 10^{-5} \cdot 2\pi \cdot 4.05 \times 10^{-2}}{1.26 \times 10^{-6}} \] \[ I = \frac{2.26 \cdot 2 \cdot 3.14159 \cdot 0.0405}{1.26 \times 10^{-6}} \] \[ I
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