solution+second+exam+fall+2005

solution+second+exam+fall+2005 - ECE 3025: Electromagnetics...

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Unformatted text preview: ECE 3025: Electromagnetics School of Electrical and Computer Engineering Georgia Institute of Technology Professor Wflliam D. Hunt Exam #2 Name: Kc November 1, 2005 Prof. William D. Hunt Total # of Points: 133pts This test is CLOSED BOOKa closed notes, no calculator but you are allowed to have the front and back of two 3"X5" index cards. Show your work Where appropriate. Short Answer: l.(5 pts) The Continuity equation relates a. A charge distribution to the induced magnetic field. Kb) Time derivative of the volume charge density to the divergence of the current density. c. A current distribution to the induced magnetic field. d. Divergence of the current density to the integral over time of the volume charge density 2.(5 pts) Laplace’s equation applies: When there is volume charge present Ll} When there is no volume charge present c. When there is a high frequency magnetic field. (1. None of the above. 3 (5 pt“) Calculation of the capacitance of a structure requires: a. Knowledge of the charge distribution in the structure. b. Knowledge of the current distribution in the structure. ,9“ Knowledge of the variation of the potential in the structure. W a and c e. b and c 4.(5 p.s)'\ The Hall effect: Is a manifestation of the force on current in the presence of a magnetic field. b. Is a manifestation of the force on current in the presence of an electric field. C. Is commonly used to analyze various types of magnetic materials. d. a and c e. b and c 5.(lO pts) Write the differential form of Ampere’s Law. Write the boundary condition which results from this law and explain What each of the components are (e. g direction: of the normal vector). ‘4 _ «3,. ,. EL 2. /’ '5 ,. ‘3 J 1 be emf“; ) = K “7 {a} A K 6 Va ' 0“”‘11" Q O‘K_(9 Z l’ 2 "* 1;: gland/C diff!!! in. “r ere—u e 6. (3 Opts) Assume the quasistatic case. Sketch each case and expieefs- the boundary conditions for the following in the most detailed, simplified form. Give an expression for the surface normal. For examnle if the Situahen calls for mannetm "01d .szvlulnlgwn. I: , 8 yaw 13w. boundary conditions, then include only the magnetic field boundary conditions. (I .x ‘3: (’W‘ J é a. A uniform dielectric sphere (E1) immersed in a conducting fluid, like mercury. An electric field is applied. b. An infinitely long conductive cylinder in air. The conductor is carrying current. c. A conductive infinite cone of angle (1 lies over an infinite ground plane. A voltage, V, is applied between the cone and the ground plane. The medium between the cone and the gromd plane is glass. 1 i . icon/I a) @{9 imitated; \3 ; ,r V he p I c I//, a. 1 “as Z» J ‘ C \ 0'“ ‘0“ L1 . I" 3 e A *— ‘tt 0 ‘ V 63, wt p833} “jg; " “i We ,9; — A 1;?" it; lei with K A ‘“L i W £3" g, r 5' w gm. {ewe 3» fia‘ v17 W‘eee2itmd a: g 1 h '4"; gar] A; i ‘9 A L w :3, I357 flee "’ f: m 1:: ' 1* tie; J I Problems: Show your work. You will receive littie or at: credit if you simply write down an answer-«even if that answer happens to be correct. You will receive far more partial credit by showing your work, even if you come up with the wrong answer. 7. Consider two perfectly perfectly conducting spheres with a dieieetrie medium of permittivity 6. between them. The inner sphere is of radius a and the outer sphere is of radius b. A voltage V0, is applied to the inner sphere with the outer sphere grounded. a. (6 pts)Sketch the configuration. What coordinate system should be used? b. (8 pts)Begin with the appropriate fonn of Laplaee’s equation and simplify as much as possible. 0. (12 points)Solve fer the potential between the two spheres. You cannot have any mmnown coefficients in your solution. (V o is known.) (1. (10 pts)Find the charge density, pg, on the surface of the outer sphere. e. «(15 point bonus question) Find the eapacitance of this/“structure. jun/:1 roarifhe‘liieu a: 9" a p ‘ gay I 3 “23" r a? ‘ 2. t f l h f I'M/it w '(S'M‘jse {MU i .l I " : r“ E: Z w? <- 3 I. ‘1‘” 3 r - u 9 ,. ‘ r ~ .6 firm J§-'”4vh!h€ J’lLt . J ram g fly I W V» have. J- h if 1 2:: iv) {L Q r _. 4, ha“ gr a v) i 3' {fl jut 32 a f 7‘ in i( r, .w‘ fl MI 5 if r l ’ ~= .7 + {J "' 1A (Lt. si.) me ., R) V ISL-ka 3"? VK: 8. Consider coaxial cable which contains two coaxial conductors. Assume the inner conductor is solid and of radius a and carries a current of I. The outer conductor is also solid and begins at radius 1) and ends at radius c and carries a current of ~1 . We have a < b < c. For the purposes of this problem, assume that the field does not go to zero inside the conductors. (5 pts) Sketch the problem and define the coordinate system and axis directions. (8 pts)F ind the magnetic field, H, inside the inner conductor. (8 13$)?in the magnetic field, H, between "the cylinders. (8 pts)Find the magnetic field, H, inside/within the outer conductor. (8 pts)Find the magnetic field, H, outside the outer conductor. If 9‘s .099 1' l? I / t . I‘m \fal'ta'é Iv“, #7 “m3 (‘ z a a» J H “e I fl Laplaciag: CYLINDBICAL vrr’:l§~{pg¥v_)+ig:p+g—i "“ ’3- -‘ (Li), :3... [J U}; E up, P" Unw— Ufiw SPHERICAL Var :ijlwm’) + 1 3 (Sin ““~.—i,7—i; '3.— ": 5'3" V Ur r3 $118819 :39 y, m" ,V Gradient: Cylindrical: VV :: flap +1916, 4, 21: az 6p [75¢ ¢ 52 Spherical: VVzéKar+i§~Vla6+ a¢ (3!” p 649 rsmfi ...
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This note was uploaded on 12/22/2011 for the course ECE 3025 taught by Professor Citrin during the Fall '08 term at Georgia Institute of Technology.

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solution+second+exam+fall+2005 - ECE 3025: Electromagnetics...

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