Question 3 [25 points] (CO2→PO2) : A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals. The physical form and construction of practical capacitors vary widely and many types of capacitor are in common use. Most capacitors contain at least two electrical conductors often in the form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, bead of metal, or an electrolyte. The dielectric medium acts to increáse the capacitor's charge capacity. Materials commonly used as dielectrics include glass, ceramic, plastic film, paper, mica, air, and oxide layers. In this context, assume there are two conducting spherical shells have radii a=5 cm and b=10 cm, respectively. The interior is a perfect dielectric for which εr = 18. (a) Calculate C. (C3 - 5 points) A first portion of the original dielectric is now removed so that εr =4.0 for 0<ϕ<π/2, a second portion of the original dielectric is now removed and replaced with a new dielectric so that εr =6.0 for π/2<ϕ <π, a third portion of the original dielectric is now removed and replaced with a new dielectric so that εr =10.0 for π<ϕ<3π/2, and a fourth portion of the original dielectric is now removed and replaced with a new dielectric so that εr =15.0 for 3π/2<ϕ<2π. (b) Illustrate the new spherical capacitor with the different dielectric regions described above. (C3 - 5 points) (c) Evaluate by how much the new capacitance C
new changes when compared with the capacitance C when the entire interior space of the capacitor is filled with a perfect dielectric of εr =18.(C4−15 points)