Insulator Metallic Shell An insulating sphere of radius 2 cm and charge O uC is surrounded by a spherical metallic shell of inner radius 5 cm and outer radius 8 cm. The outer shell has a net charge of 2 uC. The insulating sphere has a uniform volume charge density. What is the E field at 8.7 cm from the center of the insulating sphere?

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**Diagram Explanation:**

The diagram illustrates a cross-sectional view of a spherical system. It consists of:

1. **Insulating Sphere**: 
   - Radius: 2 cm.
   - Charge: 0 μC.

2. **Metallic Shell**:
   - Inner Radius: 5 cm.
   - Outer Radius: 8 cm.
   - Net Charge: 2 μC.

The insulating sphere is placed concentrically within the metallic shell. The labeling indicates the insulating material in the center and the surrounding metallic shell.

**Problem Statement:**

An insulating sphere with a radius of 2 cm and a charge of 0 μC is enclosed by a spherical metallic shell with an inner radius of 5 cm and an outer radius of 8 cm. The outer shell carries a net charge of 2 μC. The goal is to determine the electric field (E field) at a distance of 8.7 cm from the center of the insulating sphere.

**Solution Approach:**

- Apply Gauss's Law to find the electric field at a given distance outside the metallic shell.
- Consider the total enclosed charge and the symmetry of the system to solve for the electric field magnitude.
Transcribed Image Text:**Diagram Explanation:** The diagram illustrates a cross-sectional view of a spherical system. It consists of: 1. **Insulating Sphere**: - Radius: 2 cm. - Charge: 0 μC. 2. **Metallic Shell**: - Inner Radius: 5 cm. - Outer Radius: 8 cm. - Net Charge: 2 μC. The insulating sphere is placed concentrically within the metallic shell. The labeling indicates the insulating material in the center and the surrounding metallic shell. **Problem Statement:** An insulating sphere with a radius of 2 cm and a charge of 0 μC is enclosed by a spherical metallic shell with an inner radius of 5 cm and an outer radius of 8 cm. The outer shell carries a net charge of 2 μC. The goal is to determine the electric field (E field) at a distance of 8.7 cm from the center of the insulating sphere. **Solution Approach:** - Apply Gauss's Law to find the electric field at a given distance outside the metallic shell. - Consider the total enclosed charge and the symmetry of the system to solve for the electric field magnitude.
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