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Unformatted text preview: a and b , respectively, carry charges Q . The empty space between the spheres is half lled by a hemispherical shell of dielectric (of dielectric constant / ), as shown in the gure. +Q b a-Q a) Find the electric eld everywhere between the spheres. b) Calculate the surface-charge distribution on the inner sphere. c) Calculate the polarization-charge density induced on the surface of the dielectric at r = a . 6) (J 4.13) Two long, coaxial, cylindrical conducting surfaces of radii a and b ( b > a ) are lowered vertically into a liquid dielectric. If the liquid rises and average height h between the electrodes when a potential dierence V is established between them, show that the susceptibility of the liquid is e = ( b 2-a 2 ) gh ln ( b/a ) V 2 where is the density of the liquid, g is the acceleration due to gravity, and the suscep-tibility of air is neglected....
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