College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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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Can you help me with part B
![### Educational Exercise on Electric Fields
#### Problem Description
Charge \(Q\) is uniformly distributed along a thin, flexible rod of length \(L\). The rod is then bent into the semicircle shown in the figure.
#### Part A
Find an expression for the electric field \(\vec{E}\) at the center of the semicircle.
**Hint:** A small piece of arc length \(\Delta s\) spans a small angle \(\Delta \theta = \Delta s/R\), where \(R\) is the radius.
Express your answer in terms of the variables \(Q\), \(L\), unit vectors \(\hat{i}\), \(\hat{j}\), and appropriate constants.
\[
\vec{E} = \frac{Q}{2\epsilon_0 L^2} \hat{i}
\]
- **Feedback:** Correct
#### Part B
Evaluate the field strength if \(L = 12 \, \text{cm}\) and \(Q = 28 \, \text{nC}\).
Express your answer with the appropriate units.
\[
E = \text{Value} \quad \text{Units}
\]
#### Figure Description
The figure displays a semicircle with charge \(Q\) distributed uniformly along its length \(L\). The semicircle is centered at the origin of a Cartesian coordinate system, with the x-axis extending through the diameter of the semicircle.
### Key Concepts
- Understand charge distribution along a curved path.
- Apply the concept of electric fields resulting from continuous charge distributions.
- Use calculus to integrate the electric field contributions from each segment of the charged semicircle.
This exercise tests comprehension in setting up integrals for electric fields in non-linear distributions and calculating resultant vectors from symmetrical charge configurations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff29743aa-20ba-4376-81ba-ec57f5b19078%2F40b57a85-5dd2-4c9f-81c7-12bd9ebec2f2%2Fxibh3qc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Exercise on Electric Fields
#### Problem Description
Charge \(Q\) is uniformly distributed along a thin, flexible rod of length \(L\). The rod is then bent into the semicircle shown in the figure.
#### Part A
Find an expression for the electric field \(\vec{E}\) at the center of the semicircle.
**Hint:** A small piece of arc length \(\Delta s\) spans a small angle \(\Delta \theta = \Delta s/R\), where \(R\) is the radius.
Express your answer in terms of the variables \(Q\), \(L\), unit vectors \(\hat{i}\), \(\hat{j}\), and appropriate constants.
\[
\vec{E} = \frac{Q}{2\epsilon_0 L^2} \hat{i}
\]
- **Feedback:** Correct
#### Part B
Evaluate the field strength if \(L = 12 \, \text{cm}\) and \(Q = 28 \, \text{nC}\).
Express your answer with the appropriate units.
\[
E = \text{Value} \quad \text{Units}
\]
#### Figure Description
The figure displays a semicircle with charge \(Q\) distributed uniformly along its length \(L\). The semicircle is centered at the origin of a Cartesian coordinate system, with the x-axis extending through the diameter of the semicircle.
### Key Concepts
- Understand charge distribution along a curved path.
- Apply the concept of electric fields resulting from continuous charge distributions.
- Use calculus to integrate the electric field contributions from each segment of the charged semicircle.
This exercise tests comprehension in setting up integrals for electric fields in non-linear distributions and calculating resultant vectors from symmetrical charge configurations.
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