The magnitude of the magnetic field 30 cm from a long, thin, straight wire is 4 µT. What is the current through the long wire? Hint The current through the long wire is Question Help: Message instructor A.
The magnitude of the magnetic field 30 cm from a long, thin, straight wire is 4 µT. What is the current through the long wire? Hint The current through the long wire is Question Help: Message instructor A.
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![**Problem Statement:**
The magnitude of the magnetic field 30 cm from a long, thin, straight wire is 4 μT. What is the current through the long wire?
**Hint:**
[No additional content provided in image]
**Solution Input:**
The current through the long wire is _____ A.
**Help Section:**
- Question Help: [Message instructor]
**Submission:**
[Submit Question] button
---
**Explanation:**
This problem involves calculating the current in a long, thin, straight wire given the magnetic field's magnitude at a certain distance from the wire. The magnetic field (B) at a distance (r) from an infinitely long straight current-carrying wire can be calculated using the formula:
\[ B = \frac{{\mu_0 \cdot I}}{{2\pi r}} \]
where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)),
- \( I \) is the current through the wire,
- \( r \) is the distance from the wire.
Given:
- \( B = 4 \, \mu\text{T} = 4 \times 10^{-6} \, \text{T} \)
- \( r = 30 \, \text{cm} = 0.3 \, \text{m} \)
You would input these values into the formula and solve for the current \( I \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0edab40-1f13-4f88-959e-31b8927d437a%2Fefa1a6db-bed1-4b61-ad37-4fbaf31d7f6f%2Fijw73fr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The magnitude of the magnetic field 30 cm from a long, thin, straight wire is 4 μT. What is the current through the long wire?
**Hint:**
[No additional content provided in image]
**Solution Input:**
The current through the long wire is _____ A.
**Help Section:**
- Question Help: [Message instructor]
**Submission:**
[Submit Question] button
---
**Explanation:**
This problem involves calculating the current in a long, thin, straight wire given the magnetic field's magnitude at a certain distance from the wire. The magnetic field (B) at a distance (r) from an infinitely long straight current-carrying wire can be calculated using the formula:
\[ B = \frac{{\mu_0 \cdot I}}{{2\pi r}} \]
where:
- \( B \) is the magnetic field,
- \( \mu_0 \) is the permeability of free space (\(4\pi \times 10^{-7} \, \text{T}\cdot\text{m/A}\)),
- \( I \) is the current through the wire,
- \( r \) is the distance from the wire.
Given:
- \( B = 4 \, \mu\text{T} = 4 \times 10^{-6} \, \text{T} \)
- \( r = 30 \, \text{cm} = 0.3 \, \text{m} \)
You would input these values into the formula and solve for the current \( I \).
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