HW4solutions - S'a/u'ln'ofl ECE604 Homework 4 Out Tuesday...

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Unformatted text preview: S'a/u'ln'ofl ECE604 Homework 4 Out: Tuesday, February 3, 2004 (Session 7) Due: Tuesday, February 10, 2004 (Session. 9) [Students with tape delays: due according to session number] Problems numbers are from the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994). 1) 2) 3) 4) 5) 6) 7) 7.12h Give an expression for the added capacitance per unit length AND evaluate numerically. Hints: a) Use a superposition solution CD = CD1 + C132 , where $1 = Voy/ a is the solution for the parallel plate capacitor Without the extra conducting strip. b) In solving for C132 , solve separately for x 2 0 and x S 0. Once you have the solution for x 2 O , the solution for x S 0 follows almost by inspection. 0) Use your solution for $2 in computing the added capacitance. 2.5 2.6b 2.9c 2.9d 2.120 A solid dielectric cylinder of radius a and length 2L is uniformly polarized with polarization P, where P is directed axially (i.e. P = p2 ; where p = const.). Determine the electric field, E, along the cylinder axis inside and outside of the cylinder (i.e. E(z) |X=y:0 ). Hint: Identify the bound charge at the surfaces. These bound charges act as a source for E, which can be obtained through integration. 8) A sphere of radius a has electric charge distributed on its surface so that the electric field inside is uniform and given by Ei = E02 (for r < a) The sphere is hollow, i.e. a = 80 everywhere inside the sphere. The sphere is embedded in an insulator, with dielectric constants. a) Determine the surface charge density ps(9) on the surface of the sphere. Hint: First solve for the potential using Laplace’s equation and appropriate boundary conditions. b) Make a sketch showing representative E-field lines and the distribution of surface charge. Comment on the behavior of the field lines at the boundary. in}: §=‘§._+§2 . ’ '1’. is Mlzl-Ylme pbtential. Q: W3 efl‘ect 09 std-3?. Mad capadtonce is eound 11mm 2%. . 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