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2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius b and a total charge -Q. For parts a) and b), the region between the conductors (a

2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius b and a total charge -Q. For parts a) and b), the region between the conductors (a

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2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius 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 your answer from part a)) and second by integrating the energy density u of the electric field over all space. Do your answers agree? = 20 c) Now suppose the region between the conductors is filled with a dielectric with dielectric constant ‹ = 3. What is the bound charge per unit area near the inner sphere (at r = = a) and near the outer shell (at r = b)? What is the total bound charge at each surface (expressed as a fraction of the free charge Qƒ)?
Transcribed Image Text:2. In lecture we saw parallel plate and coaxial cylindrical capacitors. We can also have spherical capacitors! Consider a conducting sphere with radius a and total charge Q enclosed within a concentric hollow spherical conducting shell with radius 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 your answer from part a)) and second by integrating the energy density u of the electric field over all space. Do your answers agree? = 20 c) Now suppose the region between the conductors is filled with a dielectric with dielectric constant ‹ = 3. What is the bound charge per unit area near the inner sphere (at r = = a) and near the outer shell (at r = b)? What is the total bound charge at each surface (expressed as a fraction of the free charge Qƒ)?
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