The equipotential lines in a region of electric field are shown in the diagram below. For each path indicated below, what is the work done by the electric field in moving a charge q = +9.5 x 10 C along that path? Here Vo = +100 D 2V Vo -Vo A ov -2V0 -3Vo (a) from A to B WAB = 5.798 How is the work done by an electric field related to the potential difference between the initial and final locations? J (b) from A to C WAC = (c) from A to D WAD = ( (d) from D to C Woc -L

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**Transcription for Educational Website**

**Title: Analyzing Work Done in an Electric Field**

The equipotential lines in a region of an electric field are shown in the diagram below. For each path indicated, what is the work done by the electric field in moving a charge \( q = +9.5 \times 10^{-7} \, \text{C} \) along that path? Here, \( V_0 = +100 \, \text{V} \).

![Diagram of Equipotential Lines](image-link)

**Diagram Explanation:**

The diagram consists of a grid overlaid with curved red lines representing equipotential lines. These lines are labeled with potential values:
- \( 3V_0 \) (highest potential)
- \( 2V_0 \)
- \( V_0 \)
- \( 0V \)
- \( -V_0 \)
- \( -2V_0 \)
- \( -3V_0 \) (lowest potential)

Points A, B, C, and D are marked on the grid, each located at specific intersections of equipotential lines.

**Work Calculation Paths:**

1. **From A to B**
   \[
   W_{AB} = \text{Enter Here} \, \text{J}
   \]
   *Note: The incorrect value of 5.798 was provided. Calculate the correct work based on the potential difference.*

   **Question:** How is the work done by an electric field related to the potential difference between the initial and final locations?

2. **From A to C**
   \[
   W_{AC} = \underline{\hspace{1in}} \, \text{J}
   \]

3. **From A to D**
   \[
   W_{AD} = \underline{\hspace{1in}} \, \text{J}
   \]

4. **From D to C**
   \[
   W_{DC} = \underline{\hspace{1in}} \, \text{J}
   \]

In each case, determine the work done \( W \) using the formula related to charge and potential difference: 
\[ 
W = q \Delta V 
\]
where \( \Delta V \) is the difference between the potentials at the initial and final positions.
Transcribed Image Text:**Transcription for Educational Website** **Title: Analyzing Work Done in an Electric Field** The equipotential lines in a region of an electric field are shown in the diagram below. For each path indicated, what is the work done by the electric field in moving a charge \( q = +9.5 \times 10^{-7} \, \text{C} \) along that path? Here, \( V_0 = +100 \, \text{V} \). ![Diagram of Equipotential Lines](image-link) **Diagram Explanation:** The diagram consists of a grid overlaid with curved red lines representing equipotential lines. These lines are labeled with potential values: - \( 3V_0 \) (highest potential) - \( 2V_0 \) - \( V_0 \) - \( 0V \) - \( -V_0 \) - \( -2V_0 \) - \( -3V_0 \) (lowest potential) Points A, B, C, and D are marked on the grid, each located at specific intersections of equipotential lines. **Work Calculation Paths:** 1. **From A to B** \[ W_{AB} = \text{Enter Here} \, \text{J} \] *Note: The incorrect value of 5.798 was provided. Calculate the correct work based on the potential difference.* **Question:** How is the work done by an electric field related to the potential difference between the initial and final locations? 2. **From A to C** \[ W_{AC} = \underline{\hspace{1in}} \, \text{J} \] 3. **From A to D** \[ W_{AD} = \underline{\hspace{1in}} \, \text{J} \] 4. **From D to C** \[ W_{DC} = \underline{\hspace{1in}} \, \text{J} \] In each case, determine the work done \( W \) using the formula related to charge and potential difference: \[ W = q \Delta V \] where \( \Delta V \) is the difference between the potentials at the initial and final positions.
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