A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux De through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r> Band (b.) r < B: (a.) What is the electric flux through a sphere of radius r when r > B? Let Q = 18.8 PC 18.8 x 10-12 C and B = 7.00 cm. (Enter the answer numerically in the first box and symbolically in the second. Use the given symbols as necessary: Q, B, rand (Greek) for .) = 8.854 x 10-12 C²/(m²) DE = Nm²= (b.) What is the electric flux through a sphere of radius r when r < B? To calculate this answer, which will be a function of r, begin by answering the following questions symbolically. Use the given symbols as necessary: Q, B, r and (Greek) & for E- Question to consider: (i) What is the surface charge density, o? (ii) What is the charge enclosed, qin by the sphere of radius r (when r < B), as a function of r? (Note that is already included as part of the answer, below.) The electric flux will be a function of r (when r
A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux De through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r> Band (b.) r < B: (a.) What is the electric flux through a sphere of radius r when r > B? Let Q = 18.8 PC 18.8 x 10-12 C and B = 7.00 cm. (Enter the answer numerically in the first box and symbolically in the second. Use the given symbols as necessary: Q, B, rand (Greek) for .) = 8.854 x 10-12 C²/(m²) DE = Nm²= (b.) What is the electric flux through a sphere of radius r when r < B? To calculate this answer, which will be a function of r, begin by answering the following questions symbolically. Use the given symbols as necessary: Q, B, r and (Greek) & for E- Question to consider: (i) What is the surface charge density, o? (ii) What is the charge enclosed, qin by the sphere of radius r (when r < B), as a function of r? (Note that is already included as part of the answer, below.) The electric flux will be a function of r (when r
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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A thin, circular plate of radius B, uniform surface charge density, and total charge Q, is centered on the origin and lies in the x-y plane. What is the electric flux ΦE through a sphere of radius r, also centered on the origin, as a function of r? Consider both (a.) r > B and (b.) r < B:
![**Educational Content: Calculation of Electric Flux Through a Sphere**
**Context:**
A thin, circular plate of radius \( B \), uniform surface charge density, and total charge \( Q \), is centered on the origin and lies in the x-y plane. We need to calculate the electric flux \( \Phi_E \) through a sphere of radius \( r \), also centered on the origin, as a function of \( r \). Consider both \( (a) \, r > B \) and \( (b) \, r < B \).
---
**(a.) What is the electric flux through a sphere of radius \( r \) when \( r > B \)?**
- Given:
- \( Q = 18.8 \, \text{pC} = 18.8 \times 10^{-12} \, \text{C} \)
- \( B = 7.00 \, \text{cm} \)
- \( \varepsilon_0 = 8.854 \times 10^{-12} \, \text{C}^2/\text{(Nm}^2\text{)} \)
- Electric flux formula:
\[
\Phi_E = \frac{Q}{\varepsilon_0}
\]
**(b.) What is the electric flux through a sphere of radius \( r \) when \( r < B \)?**
To calculate this, begin by answering the following symbolic questions:
1. **Surface charge density, \( \sigma \):**
- \( \sigma = \frac{Q}{\pi B^2} \)
2. **Charge enclosed, \( q_{\text{in}} \), by the sphere of radius \( r \):**
- \( q_{\text{in}} = \sigma \times \pi r^2 \)
- \( q_{\text{in}} = \frac{Q}{B^2} r^2 \)
- **Electric flux formula (when \( r < B \)):**
\[
\Phi_E = kr^2
\]
- **Value of constant \( k \):**
- \( k = \frac{Q}{B^2 \varepsilon_0} \)
---
**Graph Explanation:**
- The graph plots electric flux \( \Phi_E \) as a function of sphere radius \( r \).
- **](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F36ba068c-5f18-4ae4-912e-4265a42ac9a7%2F4c9becaf-e52e-47b7-b892-df7c90f6f57f%2Fxvq4bw_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Calculation of Electric Flux Through a Sphere**
**Context:**
A thin, circular plate of radius \( B \), uniform surface charge density, and total charge \( Q \), is centered on the origin and lies in the x-y plane. We need to calculate the electric flux \( \Phi_E \) through a sphere of radius \( r \), also centered on the origin, as a function of \( r \). Consider both \( (a) \, r > B \) and \( (b) \, r < B \).
---
**(a.) What is the electric flux through a sphere of radius \( r \) when \( r > B \)?**
- Given:
- \( Q = 18.8 \, \text{pC} = 18.8 \times 10^{-12} \, \text{C} \)
- \( B = 7.00 \, \text{cm} \)
- \( \varepsilon_0 = 8.854 \times 10^{-12} \, \text{C}^2/\text{(Nm}^2\text{)} \)
- Electric flux formula:
\[
\Phi_E = \frac{Q}{\varepsilon_0}
\]
**(b.) What is the electric flux through a sphere of radius \( r \) when \( r < B \)?**
To calculate this, begin by answering the following symbolic questions:
1. **Surface charge density, \( \sigma \):**
- \( \sigma = \frac{Q}{\pi B^2} \)
2. **Charge enclosed, \( q_{\text{in}} \), by the sphere of radius \( r \):**
- \( q_{\text{in}} = \sigma \times \pi r^2 \)
- \( q_{\text{in}} = \frac{Q}{B^2} r^2 \)
- **Electric flux formula (when \( r < B \)):**
\[
\Phi_E = kr^2
\]
- **Value of constant \( k \):**
- \( k = \frac{Q}{B^2 \varepsilon_0} \)
---
**Graph Explanation:**
- The graph plots electric flux \( \Phi_E \) as a function of sphere radius \( r \).
- **
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