### Electric Potential Difference Calculation#### Problem Statement:A uniform electric field of magnitude 340 V/m is directed in the negative \( y \) direction as shown in the figure below. The coordinates of point \( A \) are \((-0.650, -0.200)\) m, and those of point \( B \) are \((0.350, 0.200)\) m. Calculate the electric potential difference \( V_B - V_A \) using the dashed-line path.#### Diagram Explanation:- The diagram shows a Cartesian coordinate system with points \( A \) and \( B \) marked.- Point \( A \) is located at coordinates \((-0.650, -0.200)\) m.- Point \( B \) is located at coordinates \((0.350, 0.200)\) m.- A dashed-line path connects points \( A \) and \( B \).- The electric field \( \mathbf{E} \) is represented by arrows pointing downward, indicating it is directed in the negative \( y \) direction.#### Calculation:To find the electric potential difference \( V_B - V_A \):1. **Identify position vectors:** - \( \mathbf{r_A} = (-0.650, -0.200) \) m - \( \mathbf{r_B} = (0.350, 0.200) \) m2. **Determine displacement vector \( \mathbf{d} \):** \[ \mathbf{d} = \mathbf{r_B} - \mathbf{r_A} = (0.350 - (-0.650), 0.200 - (-0.200)) = (1.000, 0.400) \ \text{m} \]3. **Dot product of \(\mathbf{E}\) and \(\mathbf{d}\) in the \( y \)-direction:** Since the electric field is in the negative \( y \) direction: \[ \mathbf{E} = (0, -340) \ \text{V/m} \] Displacement vector in the \( y \)-direction: \[ d_y = 0.200 - (-0.200) = 0.400 \ \text{m} \]4. **Calculate the potential difference \( V_B -

Given E=340 V/m Along negative y-axis A=(-0.650 , -0.200) B=(0.350,0.200) Required VB-VA

A uniform electric field of magnitude 340 V/m is directed in the negative y direction as shown in the figure below. The coordinates of point are (-0.650, -0.200) m, and those of point Ⓡare (0.350, 0.200) m. Calculate the electric potential difference V-VA using the dashed-line path. B # E ttt

A uniform electric field of magnitude 340 V/m is directed in the negative y direction as shown in the figure below. The coordinates of point are (-0.650, -0.200) m, and those of point Ⓡare (0.350, 0.200) m. Calculate the electric potential difference V-VA using the dashed-line path. B # E ttt

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### Electric Potential Difference Calculation

#### Problem Statement:
A uniform electric field of magnitude 340 V/m is directed in the negative \( y \) direction as shown in the figure below. The coordinates of point \( A \) are \((-0.650, -0.200)\) m, and those of point \( B \) are \((0.350, 0.200)\) m. Calculate the electric potential difference \( V_B - V_A \) using the dashed-line path.

#### Diagram Explanation:
- The diagram shows a Cartesian coordinate system with points \( A \) and \( B \) marked.
- Point \( A \) is located at coordinates \((-0.650, -0.200)\) m.
- Point \( B \) is located at coordinates \((0.350, 0.200)\) m.
- A dashed-line path connects points \( A \) and \( B \).
- The electric field \( \mathbf{E} \) is represented by arrows pointing downward, indicating it is directed in the negative \( y \) direction.

#### Calculation:
To find the electric potential difference \( V_B - V_A \):

1. **Identify position vectors:**
- \( \mathbf{r_A} = (-0.650, -0.200) \) m
- \( \mathbf{r_B} = (0.350, 0.200) \) m

2. **Determine displacement vector \( \mathbf{d} \):**
\[
\mathbf{d} = \mathbf{r_B} - \mathbf{r_A} = (0.350 - (-0.650), 0.200 - (-0.200)) = (1.000, 0.400) \ \text{m}
\]

3. **Dot product of \(\mathbf{E}\) and \(\mathbf{d}\) in the \( y \)-direction:**
Since the electric field is in the negative \( y \) direction:
\[
\mathbf{E} = (0, -340) \ \text{V/m}
\]
Displacement vector in the \( y \)-direction:
\[
d_y = 0.200 - (-0.200) = 0.400 \ \text{m}
\]

4. **Calculate the potential difference \( V_B -

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