< 1 of 1 > Correct Part B Evaluate the field strength if L = 12 cm and Q = 28 nC. Express your answer with the appropriate units. μA ?

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Chapter1: Units, Trigonometry. And Vectors
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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.
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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