(L10) You want to produce a magnetic field of magnitude 1.46E-3 T at a distance of 0.0450 m from a long, straight wire's center. What current do you need to apply to the wire to produce this field (in A)?
(L10) You want to produce a magnetic field of magnitude 1.46E-3 T at a distance of 0.0450 m from a long, straight wire's center. What current do you need to apply to the wire to produce this field (in A)?
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Magnetic Field Calculation for a Long, Straight Wire**
**Problem Statement:**
You want to produce a magnetic field of magnitude \(1.46 \times 10^{-3} \, \text{T}\) at a distance of \(0.0450 \, \text{m}\) from a long, straight wire's center. What current do you need to apply to the wire to produce this field (in amperes)?
**Solution:**
To determine the current required to produce the given magnetic field, you can use Ampere's Law for a long, straight wire. The magnetic field \(B\) at a distance \(r\) from a long straight wire carrying a current \(I\) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Where:
- \(B\) is the magnetic field in teslas (T)
- \(\mu_0\) is the permeability of free space (\(\mu_0 = 4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}\))
- \(I\) is the current in amperes (A)
- \(r\) is the distance from the wire in meters (m)
Rearranging this formula to solve for the current \(I\):
\[ I = \frac{2 \pi r B}{\mu_0} \]
Given:
- \(B = 1.46 \times 10^{-3} \, \text{T}\)
- \(r = 0.0450 \, \text{m}\)
- \(\mu_0 = 4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}\)
Plug in the values:
\[ I = \frac{2 \pi (0.0450 \, \text{m})(1.46 \times 10^{-3} \, \text{T})}{4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}} \]
\[ I = \frac{2 \times 0.0450 \times 1.46 \times 10^{-3}}{4 \times 10^{-7}} \]
\[ I = \frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6401e82b-1884-43b6-8725-0773860dca12%2Fa7e297db-3eaf-442f-a828-c1429a4af2fa%2F48in8fb_processed.png&w=3840&q=75)
Transcribed Image Text:**Magnetic Field Calculation for a Long, Straight Wire**
**Problem Statement:**
You want to produce a magnetic field of magnitude \(1.46 \times 10^{-3} \, \text{T}\) at a distance of \(0.0450 \, \text{m}\) from a long, straight wire's center. What current do you need to apply to the wire to produce this field (in amperes)?
**Solution:**
To determine the current required to produce the given magnetic field, you can use Ampere's Law for a long, straight wire. The magnetic field \(B\) at a distance \(r\) from a long straight wire carrying a current \(I\) is given by the formula:
\[ B = \frac{\mu_0 I}{2 \pi r} \]
Where:
- \(B\) is the magnetic field in teslas (T)
- \(\mu_0\) is the permeability of free space (\(\mu_0 = 4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}\))
- \(I\) is the current in amperes (A)
- \(r\) is the distance from the wire in meters (m)
Rearranging this formula to solve for the current \(I\):
\[ I = \frac{2 \pi r B}{\mu_0} \]
Given:
- \(B = 1.46 \times 10^{-3} \, \text{T}\)
- \(r = 0.0450 \, \text{m}\)
- \(\mu_0 = 4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}\)
Plug in the values:
\[ I = \frac{2 \pi (0.0450 \, \text{m})(1.46 \times 10^{-3} \, \text{T})}{4 \pi \times 10^{-7} \, \text{T}\cdot\text{m}/\text{A}} \]
\[ I = \frac{2 \times 0.0450 \times 1.46 \times 10^{-3}}{4 \times 10^{-7}} \]
\[ I = \frac{
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