An isolated charged conducting sphere has a radius R = 13.0 cm. At a distance of r = 24.0 cm from the center of the sphere the electric field due to the sphere has a magnitude of E= 4.90 × 104 N/C. (a) What is its surface charge density (in μC/m²)? μC/m² (b) What is its capacitance (in pF)? pF (c) What If? A larger sphere of radius 26.0 cm is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system? DF

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**Problem Statement:**

An isolated charged conducting sphere has a radius \( R = 13.0 \, \text{cm} \). At a distance of \( r = 24.0 \, \text{cm} \) from the center of the sphere, the electric field due to the sphere has a magnitude of \( E = 4.90 \times 10^4 \, \text{N/C} \).

**Questions:**

(a) What is its surface charge density (in \(\mu \text{C/m}^2\))?
- Answer: \(\underline{\phantom{000}}\) \(\mu \text{C/m}^2\)

(b) What is its capacitance (in pF)?
- Answer: \(\underline{\phantom{000}}\) pF

(c) *What If?* A larger sphere of radius \( 26.0 \, \text{cm} \) is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system?
- Answer: \(\underline{\phantom{000}}\) pF
Transcribed Image Text:**Problem Statement:** An isolated charged conducting sphere has a radius \( R = 13.0 \, \text{cm} \). At a distance of \( r = 24.0 \, \text{cm} \) from the center of the sphere, the electric field due to the sphere has a magnitude of \( E = 4.90 \times 10^4 \, \text{N/C} \). **Questions:** (a) What is its surface charge density (in \(\mu \text{C/m}^2\))? - Answer: \(\underline{\phantom{000}}\) \(\mu \text{C/m}^2\) (b) What is its capacitance (in pF)? - Answer: \(\underline{\phantom{000}}\) pF (c) *What If?* A larger sphere of radius \( 26.0 \, \text{cm} \) is now added so as to be concentric with the first sphere. What is the capacitance (in pF) of the two-sphere system? - Answer: \(\underline{\phantom{000}}\) pF
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