Question: A solid conducting sphere of radius (R=10 mathrm{~cm}) is embedded in an electrically neutral nonconducting spherical shell that has inner radius (R), outer radius (2

A solid conducting sphere of radius $R=10 \mathrm{~cm}$ is embedded in an electrically neutral nonconducting spherical shell that has inner radius $R$, outer radius $2 R$, and is made of a material having dielectric constant $\kappa$. The potential at the center of the sphere is $540 \mathrm{~V}$. The electric field at the outer surface of the shell is directed away from the surface of the shell, and has a magnitude of $900 \mathrm{~V} / \mathrm{m}$. What are

(a) the dielectric constant of the shell

(b) the electric charge on the sphere?

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