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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 .
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