The electric field must be zero inside a conductor in electrostatic equilibrium, but not inside an insulator. It turns out that we can still apply Gauss's law to a Gaussian surface that is entirely within an insulator by replacing the right-hand side of Gauss's law, ${\mathrm{Q}}_{\text{in}}/{\mathrm{ϵ}}_0$, with ${\mathrm{Q}}_{\text{in}}/\mathrm{ϵ}$, where $\mathrm{ϵ}$ is the permittivity of the material. (Technically,${\mathrm{ϵ}}_0$ is called the vacuum permittivity.) Suppose that a $50\mathrm{nC}$ point charge is surrounded by a thin, $32-\mathrm{cm}$-diameter spherical rubber shell and that the electric field strength inside the rubber shell is$2500\mathrm{N}/\mathrm{C}$ . What is the permittivity of rubber$?$

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