The square surface shown in the figure measures 3.5 mm on each side. It is immersed in a uniform electric field with magnitude E = 1400 N/C and with field lines at an angle of 35° with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface. Normal 4
The square surface shown in the figure measures 3.5 mm on each side. It is immersed in a uniform electric field with magnitude E = 1400 N/C and with field lines at an angle of 35° with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface. Normal 4
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![### Electric Flux Calculation
The square surface shown in the figure measures 3.5 mm on each side. It is immersed in a uniform electric field with magnitude \( E = 1400 \, \text{N/C} \) and with field lines at an angle of \( 35^\circ \) with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface.
**Diagram Explanation:**
The image shows a green square surface with a vector labeled "Normal" pointing perpendicularly outward from the surface. The electric field lines are depicted as blue lines crossing the surface at an angle of \( 35^\circ \) relative to the normal.
**Steps to Calculate Electric Flux:**
1. **Electric Flux (\( \Phi_E \)) Formula:**
\[
\Phi_E = E \cdot A \cdot \cos(\theta)
\]
2. **Given Values:**
- Electric field magnitude, \( E = 1400 \, \text{N/C} \)
- Side length of the square, \( a = 3.5 \, \text{mm} = 3.5 \times 10^{-3} \, \text{m} \)
- Angle with the normal, \( \theta = 35^\circ \)
3. **Calculate the Area (\( A \)) of the Square:**
\[
A = a^2 = (3.5 \times 10^{-3} \, \text{m})^2 = 1.225 \times 10^{-5} \, \text{m}^2
\]
4. **Calculate \( \cos(35^\circ) \) using a calculator:**
\[
\cos(35^\circ) \approx 0.819
\]
5. **Substitute the values into the flux formula:**
\[
\Phi_E = 1400 \, \text{N/C} \times 1.225 \times 10^{-5} \, \text{m}^2 \times 0.819
\]
6. **Calculate the result:**
\[
\Phi_E \approx 0.014 \, \text{N}\cdot\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe462800b-ac16-4590-bafb-82d68c005ec5%2F876b2d5e-fe6c-4dfd-9c81-f1d22e83b5c2%2Fk0ihvzc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Electric Flux Calculation
The square surface shown in the figure measures 3.5 mm on each side. It is immersed in a uniform electric field with magnitude \( E = 1400 \, \text{N/C} \) and with field lines at an angle of \( 35^\circ \) with a normal to the surface, as shown. Take that normal to be "outward," as though the surface were one face of a box. Calculate the electric flux through the surface.
**Diagram Explanation:**
The image shows a green square surface with a vector labeled "Normal" pointing perpendicularly outward from the surface. The electric field lines are depicted as blue lines crossing the surface at an angle of \( 35^\circ \) relative to the normal.
**Steps to Calculate Electric Flux:**
1. **Electric Flux (\( \Phi_E \)) Formula:**
\[
\Phi_E = E \cdot A \cdot \cos(\theta)
\]
2. **Given Values:**
- Electric field magnitude, \( E = 1400 \, \text{N/C} \)
- Side length of the square, \( a = 3.5 \, \text{mm} = 3.5 \times 10^{-3} \, \text{m} \)
- Angle with the normal, \( \theta = 35^\circ \)
3. **Calculate the Area (\( A \)) of the Square:**
\[
A = a^2 = (3.5 \times 10^{-3} \, \text{m})^2 = 1.225 \times 10^{-5} \, \text{m}^2
\]
4. **Calculate \( \cos(35^\circ) \) using a calculator:**
\[
\cos(35^\circ) \approx 0.819
\]
5. **Substitute the values into the flux formula:**
\[
\Phi_E = 1400 \, \text{N/C} \times 1.225 \times 10^{-5} \, \text{m}^2 \times 0.819
\]
6. **Calculate the result:**
\[
\Phi_E \approx 0.014 \, \text{N}\cdot\
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