6. A spherical capacitor is composed of a solid conducting sphere concentric with a larger spherical conducting shell. The inner conductor has positive total charge Q and radius R. The outer conductor has negative total charge -Q, inner radius 3R, and outer radius 4R. The space between the conductors is filled with two spherical dielectric shells. The dielectric in the region R
6. A spherical capacitor is composed of a solid conducting sphere concentric with a larger spherical conducting shell. The inner conductor has positive total charge Q and radius R. The outer conductor has negative total charge -Q, inner radius 3R, and outer radius 4R. The space between the conductors is filled with two spherical dielectric shells. The dielectric in the region R
Related questions
Question
Transcribed Image Text:### Problem 6: Spherical Capacitor with Dielectric
A spherical capacitor is composed of a solid conducting sphere concentrically placed within a larger spherical conducting shell. The following characteristics define the setup:
- **Inner Conductor:**
- Charge: Positive, total charge \( Q \)
- Radius: \( R \)
- **Outer Conductor:**
- Charge: Negative, total charge \( -Q \)
- Inner Radius: \( 3R \)
- Outer Radius: \( 4R \)
The space between the conductors is filled with two spherical dielectric shells:
- **First Dielectric Region:**
- Region: \( R < r < 2R \)
- Dielectric Constant: \( K_1 = 6 \)
- **Second Dielectric Region:**
- Region: \( 2R < r < 3R \)
- Dielectric Constant: \( K_2 = 2 \)
#### Diagram Description
A cross-sectional view of the spherical capacitor system is shown with colored regions:
- Inner conductor at radius \( R \)
- First dielectric shell in green from \( R \) to \( 2R \)
- Second dielectric shell in blue from \( 2R \) to \( 3R \)
- Outer conductor from \( 3R \) to \( 4R \)
#### Tasks
(a) **Electric Field Calculation:**
Find the electric field in the regions:
- \( R < r < 2R \)
- \( 2R < r < 3R \)
(b) **Capacitance Calculation:**
Determine the capacitance of this capacitor system.
(c) **Bound Surface Charge Density:**
Calculate the bound surface charge density at:
- \( r = R \)
- \( r = 2R \)
- \( r = 3R \)
This problem facilitates understanding of electric fields in dielectric materials and the behavior of capacitors with complex geometries.
Expert Solution
Part a)
Step by step
Solved in 3 steps
