Walker, Halliday & Resnick — Capacitance: Problem 49

49 The space between two concentric conducting spherical shells of radii $b = 1.70 \text{ cm}$ and $a = 1.20 \text{ cm}$ is filled with a substance of dielectric constant $\kappa = 6.91$. A potential difference $V = 73.0 \text{ V}$ is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge $q$ on the inner shell, and (c) the charge $q'$ induced along the surface of the inner shell.