Charges q, and 92 are placed on the y-axis at y = 0 and y = 25.1 m, respectively. If q, = -46.8 pC and q2= +64 pC, determine the net flux through a spherical surface (radius = 9.5 m) centered on the origin. Round your answer to 2 decimal places.
Charges q, and 92 are placed on the y-axis at y = 0 and y = 25.1 m, respectively. If q, = -46.8 pC and q2= +64 pC, determine the net flux through a spherical surface (radius = 9.5 m) centered on the origin. Round your answer to 2 decimal places.
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![### Problem Statement:
Charges \( q_1 \) and \( q_2 \) are placed on the y-axis at \( y = 0 \) and \( y = 25.1 \) m, respectively. If \( q_1 = -46.8 \) pC and \( q_2 = +64 \) pC, determine the net flux through a spherical surface (radius = \( 9.5 \) m) centered on the origin.
Round your answer to 2 decimal places.
#### Answer:
\[ \text{Add your answer} \]
### Explanation:
Given:
- \( q_1 = -46.8 \) pC (placed at \( y = 0 \) m)
- \( q_2 = +64 \) pC (placed at \( y = 25.1 \) m)
- Radius of the spherical surface \( = 9.5 \) m
The objective is to determine the net electric flux through the spherical surface centered at the origin. The concept of electric flux can be tackled using Gauss's Law, which states:
\[ \Phi_E = \frac{q_{\text{enc}}}{\epsilon_0} \]
where \( q_{\text{enc}} \) is the enclosed charge within the Gaussian surface and \( \epsilon_0 \) is the permittivity of free space (\( \approx 8.85 \times 10^{-12} \, \text{F/m} \)).
The charge \( q_2 \) is located outside the spherical surface (as 25.1 m > 9.5 m), so it does not contribute to the enclosed charge. Therefore, only \( q_1 \) is inside the spherical surface:
\[
q_{\text{enc}} = q_1 = -46.8 \, \text{pC} = -46.8 \times 10^{-12} \, \text{C}
\]
Using Gauss's Law to find the net flux \( \Phi_E \):
\[
\Phi_E = \frac{q_{\text{enc}}}{\epsilon_0} = \frac{-46.8 \times 10^{-12} \, \text{C}}{8.85 \times 10^{-12} \, \text{F/m}}
\]
Upon calculating:
\[
\Phi_E \approx -5](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd447342a-76d3-44af-918e-aa75820122eb%2Ff0d2a006-d4c1-4259-82d3-f4fce12b11f9%2Fgwdf40m.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
Charges \( q_1 \) and \( q_2 \) are placed on the y-axis at \( y = 0 \) and \( y = 25.1 \) m, respectively. If \( q_1 = -46.8 \) pC and \( q_2 = +64 \) pC, determine the net flux through a spherical surface (radius = \( 9.5 \) m) centered on the origin.
Round your answer to 2 decimal places.
#### Answer:
\[ \text{Add your answer} \]
### Explanation:
Given:
- \( q_1 = -46.8 \) pC (placed at \( y = 0 \) m)
- \( q_2 = +64 \) pC (placed at \( y = 25.1 \) m)
- Radius of the spherical surface \( = 9.5 \) m
The objective is to determine the net electric flux through the spherical surface centered at the origin. The concept of electric flux can be tackled using Gauss's Law, which states:
\[ \Phi_E = \frac{q_{\text{enc}}}{\epsilon_0} \]
where \( q_{\text{enc}} \) is the enclosed charge within the Gaussian surface and \( \epsilon_0 \) is the permittivity of free space (\( \approx 8.85 \times 10^{-12} \, \text{F/m} \)).
The charge \( q_2 \) is located outside the spherical surface (as 25.1 m > 9.5 m), so it does not contribute to the enclosed charge. Therefore, only \( q_1 \) is inside the spherical surface:
\[
q_{\text{enc}} = q_1 = -46.8 \, \text{pC} = -46.8 \times 10^{-12} \, \text{C}
\]
Using Gauss's Law to find the net flux \( \Phi_E \):
\[
\Phi_E = \frac{q_{\text{enc}}}{\epsilon_0} = \frac{-46.8 \times 10^{-12} \, \text{C}}{8.85 \times 10^{-12} \, \text{F/m}}
\]
Upon calculating:
\[
\Phi_E \approx -5
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