(Originais Teachy 2023) - Question Medium of Physics

In a research in the area of renewable energy, a group of scientists developed an energy storage device using a spherical capacitor. This capacitor consists of two concentric conducting spheres, with the inner sphere having a radius R1 and the outer sphere having a radius R2. Consider that the space between the two spheres is filled with a dielectric material, which has an electrical permittivity ε. a) Calculate the capacitance C of the spherical capacitor in terms of R1, R2, and ε. b) Suppose R1 is 5 cm, R2 is 10 cm, and ε is equal to the electrical permittivity of vacuum (ε = 8.85 × 10⁻¹² F/m). Determine the capacitance C of the capacitor. c) Describe the relationship between capacitance and the energy stored in the capacitor and discuss, from the perspective of sustainability, how the device developed by the scientists contributes to actions in the field of renewable energy.