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Unformatted text preview: HW-7 P(r ) kr , where k is a constant. 1. A sphere of radius R carries a polarization
(a) Calculate the bound charge b and b. (b) Find the field inside and outside the sphere. 2. The space between the plate a parallel-plate capacitor is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab 1 has a dielectric constant r1, and slab 2 has a dielectric constant r2. The free charge density on the top plate is and on the bottom plate is -. (a) Find the electric displacement in each slab. (b) Find the electric field in each slab. (c) Find the polarization in each slab. (d) Find the potential difference between the plates. (e) Find the location and amount of all bound charge. (f) Now that you know all the charge (free and bound), recalculate the field in each slab, and confirm your answer to (b). 3. At the interface between one linear dielectric and another the electric field lines bend. Show that tan 2 2 tan1 2 Assuming there is no free charge at the boundary. 4. Two long coaxial cylindrical metal tubes (inner radius a, outer radius b) stand vertically in a tank of dielectric oil (susceptibility e, mass density ). The inner one is maintained at potential V, and the outer one is grounded. The voltage raises the oil level inside the tube to a height h. (a) Find the capacitance of the cylinder. (b) What is the lifting force to the oil inside the tube by the capacitor? (c) What is the height of the oil h? (d) After the oil level is raised to the height of h, what’s the extra electric energy pumped into the capacitor? Is this amount equal to the gravitational energy gain of the oil? ...
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