(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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**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{
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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