2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider aconducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell withradius 6 and a total charge -Q. For parts a) and b), the region between the conductors (a < r < b) is empty (vacuum).a) Find an expression for the capacitance of a spherical capacitor. Is it geometric as we expect?b) Find an expression for the energy stored by the spherical capacitor first by using U (just replace C by youranswer from part a)) and second by integrating the energy density u of the electric field over all space. Do your answersagree?=20c) Now suppose the region between the conductors is filled with a dielectric with dielectric constant ‹ = 3. What is thebound charge per unit area near the inner sphere (at r = = a) and near the outer shell (at r = b)? What is the total boundcharge at each surface (expressed as a fraction of the free charge Qƒ)?

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Answered: 2. In lecture we saw parallel plate and…

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A spherical capacitor consists of an inner spherical shell of radius R1 and an outer spherical shell of radius R2, as shown above. Our goal is to calculate the capacitance of this configuration of electrodes.To start, suppose the inner sphere has a charge +Q and the outer sphere an equal but opposite charge -Q. Find the capacitance using the following steps:1. Use Gauss's law to find an expression for the electric field in the region between the two spheres.2. Find an expression for the potential difference between the spheres from the electric field (you'll have to integrate the electric field from the negative electrode to the positive one).3. Calculate the capacitance from C = Q / ΔV.Suppose in this case that R1 = 2.00 cm and R2 = 4.30 cm. What is the value of the capacitance?