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# hw03 - a and b respectively carry charges ± Q The empty...

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Princeton University—Physics 501 Problem Set 3 Due: Oct. 11, 2011 1) A uniformly charged sphere of radius R total charge q , and dielectric constant 0 = 1 is imbedded in a dielectric of permittivity . What is the polarization charge density induced on the surface of the sphere? 2) An infinitely long circular cylinder of radius a and dielectric constant is placed with its axis perpendicular to an electric field ~ E . The electric field is uniform in regions of space very far away from the cylinder. Find the electric field inside and outside the cylinder and the bound surface-charge density on the cylinder. 3) A charge q is brought from infinity to a distance d from a sphere of radius a and dielectric constant . What is the work required? (Check your answer by considering the limiting cases = 1 and = .) 4) R Consider the case of a spherical cavity of radius R embedded in an otherwise homoge- neous medium of dielectric constant . At the center of the cavity is a point dipole of moment ~ p . Solve for the electric field everywhere. 5) (J 4.10) Two concentric conducting spheres of inner and outer radii

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Unformatted text preview: a and b , respectively, carry charges ± Q . The empty space between the spheres is half ﬁlled by a hemispherical shell of dielectric (of dielectric constant ±/± ), as shown in the ﬁgure. +Q b a-Q a) Find the electric ﬁeld 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 diﬀerence V is established between them, show that the susceptibility of the liquid is χ e = ( b 2-a 2 ) ρgh ln ( b/a ) ± V 2 where ρ 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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