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![The figure below shows a box-shaped closed surface with one of its edges lying on the x-axis, and its left edge located at \( x = a \). The sides have lengths \( a = b = 0.500 \, \text{m} \) and \( c = 0.750 \, \text{m} \).
Throughout the region, there is a nonuniform electric field given by:
\[
\vec{E} = (3.50 \, \text{N/C} + (2.20 \, \frac{\text{N}}{\text{m}^2 \cdot \text{C}}) x^2) \hat{i}
\]
where \( x \) is in meters. +x-direction.
### Diagram
The diagram shows a rectangular box outlined with dimensions labeled as \( c \), \( a \), and \( b \) along the y, x, and z axes respectively. The electric field \( \vec{E} \) is indicated by an arrow pointing in the positive x-direction.
### Instructions
Calculate the net electric flux by showing your calculation of the electric flux through each of the 6 faces of the box-shaped closed surface. You can choose how you label each face. For example, you can label the faces as Face 1-6, or front face, back face, left face, etc. This must be clearly labeled in your work.
### Tasks
a) Face 1
b) Face 2
c) Face 3
d) Face 4
e) Face 5
f) Face 6
g) Net Electric Flux through the closed surface (add the electric flux from each face)](https://content.bartleby.com/qna-images/question/0f0c4e77-fecd-4d18-90ed-9b329310f28f/1a18a01e-cd48-4438-960e-f6a7d065d61e/dfyr0ks_processed.png)
Transcribed Image Text:The figure below shows a box-shaped closed surface with one of its edges lying on the x-axis, and its left edge located at \( x = a \). The sides have lengths \( a = b = 0.500 \, \text{m} \) and \( c = 0.750 \, \text{m} \).
Throughout the region, there is a nonuniform electric field given by:
\[
\vec{E} = (3.50 \, \text{N/C} + (2.20 \, \frac{\text{N}}{\text{m}^2 \cdot \text{C}}) x^2) \hat{i}
\]
where \( x \) is in meters. +x-direction.
### Diagram
The diagram shows a rectangular box outlined with dimensions labeled as \( c \), \( a \), and \( b \) along the y, x, and z axes respectively. The electric field \( \vec{E} \) is indicated by an arrow pointing in the positive x-direction.
### Instructions
Calculate the net electric flux by showing your calculation of the electric flux through each of the 6 faces of the box-shaped closed surface. You can choose how you label each face. For example, you can label the faces as Face 1-6, or front face, back face, left face, etc. This must be clearly labeled in your work.
### Tasks
a) Face 1
b) Face 2
c) Face 3
d) Face 4
e) Face 5
f) Face 6
g) Net Electric Flux through the closed surface (add the electric flux from each face)
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