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A small conducting spherical shell with inner radius \(a\) and outer radius \(b\) is concentric with a larger conducting spherical shell with inner radius \(c\) and outer radius \(d\).

What is the relationship between the radii of the two shells?

Answer :

Final Answer:

The relationship between the radii of the two conducting spherical shells is that the inner radius 'a' of the smaller shell is equal to the inner radius 'c' of the larger shell, and the outer radius 'b' of the smaller shell is equal to the outer radius 'd' of the larger shell.

Explanation:

  • The situation described involves two concentric spherical shells, one smaller and one larger. When dealing with concentric spheres, it means that their centers coincide.

In this case, the radii of the two shells have a straightforward relationship:

  • The inner radius 'a' of the smaller shell matches the inner radius 'c' of the larger shell.
  • Similarly, the outer radius 'b' of the smaller shell matches the outer radius 'd' of the larger shell.

  • This relationship means that the two spherical shells share the same center, with the larger shell fully encompassing the smaller one. This configuration is often used in physics and engineering, particularly in problems involving electrostatics and conductors, as it simplifies the analysis of electric fields and charges.

  • In summary, the radii of the two conducting spherical shells are related in a way where the inner and outer radii of the smaller shell are equal to the inner and outer radii of the larger shell, respectively, indicating a concentric configuration.

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