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Unformatted text preview: Sd/Q'H'on ECE604 Homework 3
Out: Tuesday, January 25, 2005
Due: Tuesday, February 1, 2005 Note: There is now a class website at http://shay.ecn.purdue.edu/~ee604/. Problem sets,
solutions, and other handouts will be posted there. These problems are from Chapter 1 of the text by Ramo, Whinnery and Van Duzer (3rd edition, 1994) 1)
2)
3)
4)
5)
6) 7) 7.9a 7.11a parts (i) and (ii) only. Assume both functions have period L. 7.1 lb 7.12a 7.12b 7 .12e Note: Make sure you can identify all the important boundary conditions before you jump into the math. A conductor on a circuit board has width W and carries a current I. The conductivity of the conductor is 0'. There is a small hole of radius a at the center of the conductor. The
thickness t of the conductor is small compared to a. (Therefore this problem may be
treated as a twodimensional problem in cylindrical coordinates.) Assume the current is V
DC. You may also assume that the width of the circuit board W is large compared to the
hole radius (W>>a). Let the coordinate origin be at the center of the hole. (i) Sketch qualitatively the sheet current density J S (units are A/m) in the vicinity of the
hole. (The sheet current density is the uniform current density J integrated over the thickness of the conductor, that is J S = J Xt ) (ii) Derive an expression for J 8. Express your answer in terms of I, W, r and 4). (iii) What is the maximum magnitude of JS? Express your answer in terms of I and W.
(The answer does not include the hole radius a.) Note that the maximum should be
located along the x = 0 line (where the current is maximally constricted). (iv) Give an expression for the sheet surface charge density (units Coulomb/m) along the
edge of the hole. . I . 3. = 'L‘la In calindrical coordinates WtUn :9, O,
‘ L . ‘  Letting 31‘: 20') Rat); ’ves R3? ‘ ' u: J¢z I a" c. We Have two AWecential eQuaﬁons . ., 31, F; + n‘F‘4, = o (harmonic «2%. Wrist» solqtion )._
=¢=.c3¢os'nd> + C4sﬁnnd) ' 4H] _ _
 ' ' dz 'JPA [c.rnr"'+c,,r(n)e _ .
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=V93é—I), géxcL .
__.;_ o % L 3%; ¥wiscven30 b,.=o {’Oralln 1
4(1)=o.o+,.§ancos3='—EEZ‘ L ‘
an = t Mum = afﬁx)“ = 2.;3fvm ELL) dx = N5 g
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~11“): 0.. + imam”? + mam”? )dx
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= 41—?)me = _ __ i‘”: [it EJ521153)
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= g (’7? ' 5/0,?) was; ) w my): gm? ) . a
' Ir l' I?" 7Lg~u(a,'7) CFC: . 'HZb it 3 .av, '5‘” ,
§ § Obtain “total sduﬁon as §= §.+§; when: £13
I‘=() ‘=O
so‘ubion 09 Rob. 'Ilza— and E is soltglﬁon 09 POHern shown
“" a: °' in 4.6%. Far 7.5;, need repeated. zeros in x direction . I §m = (Aeoskx +Bsuhlgx)(c.coshk5 +Dsu'nh kg)
_B_.__C__. Potarb'al 53mmetﬁc in 7‘ so 830. §=o at x =10.
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§=o is“ it" =' (A (:05ka + Bsa'm kx)CCwosh L5 +‘ 195th us)
Since §(0.5)=o'and §Cx,o)=o,‘~A=.:c.=.o ’
O '5 i=0 5 cas‘mg'xsﬂﬂ I m:' N
 ‘%L»?k,¢"_°°‘k“s‘f"hk5=9. Thus lax3:; (VI 066)
:.§ =:..§°”$3”§'§*5‘”“€% . .
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 Spring '08
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 Electromagnet, Electric charge, Van Duzer, j S, Ramo, c» shah

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