There are two thin, hollow concentric spherical shells. The inner shell is charged with 8.0 nC and has a radius of 1.1 cm, while the outer shell is charged with -4.9 nC and has a radius of 8.5 cm. What is the electric potential due to the spheres at a radius of 4.5 cm? Give your answer in units of kV, with a reference point for the potential very far away from the shells. Each shell is uniformly charged.

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### Electric Potential of Concentric Spherical Shells

**Problem Statement:**
There are two thin, hollow concentric spherical shells. The inner shell is charged with 8.0 nC and has a radius of 1.1 cm, while the outer shell is charged with -4.9 nC and has a radius of 8.5 cm. What is the electric potential due to the spheres at a radius of 4.5 cm?

**Task:**
Calculate the electric potential in units of kV at a distance of 4.5 cm from the center of the shells. The reference point for the potential is very far from the shells. Assume each shell is uniformly charged.

**Solution Approach:**
1. **Identify Charged Regions:**
   - Inner Shell: Charge = 8.0 nC, Radius = 1.1 cm
   - Outer Shell: Charge = -4.9 nC, Radius = 8.5 cm

2. **Determine Electric Potential:**
   - Use the formula for electric potential due to a point charge and integrate over the spherical shell geometry.
   - Calculate the potential contribution at 4.5 cm, considering the charge values and radii.

3. **Reference Point:**
   - The potential is zero at a point infinitely far from the shells.

**Conclusion:**
Summarize the calculated electric potential at 4.5 cm in kilovolts (kV), describing how the superposition of potentials from each shell contributes to the final result.
Transcribed Image Text:### Electric Potential of Concentric Spherical Shells **Problem Statement:** There are two thin, hollow concentric spherical shells. The inner shell is charged with 8.0 nC and has a radius of 1.1 cm, while the outer shell is charged with -4.9 nC and has a radius of 8.5 cm. What is the electric potential due to the spheres at a radius of 4.5 cm? **Task:** Calculate the electric potential in units of kV at a distance of 4.5 cm from the center of the shells. The reference point for the potential is very far from the shells. Assume each shell is uniformly charged. **Solution Approach:** 1. **Identify Charged Regions:** - Inner Shell: Charge = 8.0 nC, Radius = 1.1 cm - Outer Shell: Charge = -4.9 nC, Radius = 8.5 cm 2. **Determine Electric Potential:** - Use the formula for electric potential due to a point charge and integrate over the spherical shell geometry. - Calculate the potential contribution at 4.5 cm, considering the charge values and radii. 3. **Reference Point:** - The potential is zero at a point infinitely far from the shells. **Conclusion:** Summarize the calculated electric potential at 4.5 cm in kilovolts (kV), describing how the superposition of potentials from each shell contributes to the final result.
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