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An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density...

An insulated spherical shell of inner radius a1 and outer radius a2 has a charge density ρ=6r C/m4.

(a) (2 pts.) Based on the symmetry of the situation, describe the Gaussian surface (if any) that could be used to find the electric field inside the spherical shell.

(b) (3 pts.) Starting from the definition of charge enclosed, briefly derive the integral expression for the charge enclosed inside a Gaussian surface within the insulated spherical shell for the given charge density. Once you have this expression, solve the integral.

(c) (2 pts.) Derive an expression for the electric field outside the spherical shell.

(d) (3 pts.) Briefly show how you would find the electric potential inside the insulated spherical shell at a radius r from its center. Start by writing the entire expression in general, then applying the specific expressions for this situation. (You do not need to solve this expression!)

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genius_generous answered 2 years ago
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