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
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb234898a-ca00-4740-ae3d-79576f672843%2Face50e96-20c3-4588-95c8-50d129a7714b%2Fiph6wo_processed.jpeg&w=3840&q=75)
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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