Find the magnetic field at P produced by this current element. Enter the z, y, and z components of the magnetic field in teslas separated by commas.
Find the magnetic field at P produced by this current element. Enter the z, y, and z components of the magnetic field in teslas separated by commas.
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter29: Magnetic Fields
Section: Chapter Questions
Problem 29.31P
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![**Educational Website Content**
---
### Magnetic Field Calculation from a Current Element
#### Problem Statement
A short current element \(\vec{d\mathbf{l}} = (0.500 \, \text{mm}) \, \hat{\mathbf{j}}\) carries a current of \(5.30 \, \text{A}\) in the same direction as \(\vec{d\mathbf{l}}\). Point \(P\) is located at \(\vec{r} = (-0.730 \, \text{m}) \, \hat{\mathbf{i}} + (0.390 \, \text{m}) \, \hat{\mathbf{k}}\).
#### Part A
**Task:**
Find the magnetic field at \(P\) produced by this current element.
Enter the \(x\), \(y\), and \(z\) components of the magnetic field in teslas separated by commas.
#### Input Box:
\[ dB_x, dB_y, dB_z = \, \text{[Input Box]} \, \text{T} \]
**Buttons/Tools:**
- Submit Button
- Request Answer
- Provide Feedback
- General Calculation Tools (Vector, Symbol, etc.)
#### Navigation:
- **Next** Button to proceed to subsequent part.
---
### Detailed Steps for Solving:
1. **Determine the Cross Product:**
\[
\vec{dB} = \frac{\mu_0}{4\pi} \frac{I (\vec{d\mathbf{l}} \times \vec{r})}{r^3}
\]
where \(\vec{d\mathbf{l}} = (0.500 \, \text{mm}) \, \hat{\mathbf{j}}\) and \(\vec{r} = (-0.730 \, \text{m}) \, \hat{\mathbf{i}} + (0.390 \, \text{m}) \, \hat{\mathbf{k}}\).
2. **Calculate \(r\) and \(r^3\):**
\[
r = \sqrt{(-0.730)^2 + (0.390)^2}
\]
\[
r^3 = (r)^3
\]
3. **Cross Product Calculation:**
\[
\vec{d\mathbf{l}} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0a59c95-d278-4231-b93f-c228b6025027%2Ff5544a42-b73b-4d00-beed-8dec5cf2d5ba%2Flkp7z7e.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
---
### Magnetic Field Calculation from a Current Element
#### Problem Statement
A short current element \(\vec{d\mathbf{l}} = (0.500 \, \text{mm}) \, \hat{\mathbf{j}}\) carries a current of \(5.30 \, \text{A}\) in the same direction as \(\vec{d\mathbf{l}}\). Point \(P\) is located at \(\vec{r} = (-0.730 \, \text{m}) \, \hat{\mathbf{i}} + (0.390 \, \text{m}) \, \hat{\mathbf{k}}\).
#### Part A
**Task:**
Find the magnetic field at \(P\) produced by this current element.
Enter the \(x\), \(y\), and \(z\) components of the magnetic field in teslas separated by commas.
#### Input Box:
\[ dB_x, dB_y, dB_z = \, \text{[Input Box]} \, \text{T} \]
**Buttons/Tools:**
- Submit Button
- Request Answer
- Provide Feedback
- General Calculation Tools (Vector, Symbol, etc.)
#### Navigation:
- **Next** Button to proceed to subsequent part.
---
### Detailed Steps for Solving:
1. **Determine the Cross Product:**
\[
\vec{dB} = \frac{\mu_0}{4\pi} \frac{I (\vec{d\mathbf{l}} \times \vec{r})}{r^3}
\]
where \(\vec{d\mathbf{l}} = (0.500 \, \text{mm}) \, \hat{\mathbf{j}}\) and \(\vec{r} = (-0.730 \, \text{m}) \, \hat{\mathbf{i}} + (0.390 \, \text{m}) \, \hat{\mathbf{k}}\).
2. **Calculate \(r\) and \(r^3\):**
\[
r = \sqrt{(-0.730)^2 + (0.390)^2}
\]
\[
r^3 = (r)^3
\]
3. **Cross Product Calculation:**
\[
\vec{d\mathbf{l}} \
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