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ece312_au10_exam1sol

# ece312_au10_exam1sol - Problem 1 13 parts 40 points A...

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Unformatted text preview: Problem 1 13 parts, 40 points) A current density .7 = 52 A/m2 ﬂows through the cross section of an inﬁnitely long hollow cylinder as shown. The hollow cylinder has inner radius 10 cm, outer radius 25 cm, and u = 1000 no, While the space inside and outside the cylinder has it = no. Be sure to include both magnitude and direction when providing vector answers. 3 ﬂows in hollow cylinder cross section (inﬁnitely long) (a) Find the magnetic ﬁeld intensity on the axis of the cylinder (Le. at r = 0 ). (10 points) A A F \$.38: #:“w m m it sin ens Magnesiecmi «K its ‘ ' a mrgcmtiiiﬁr b £32; iwﬁsim ,, easements ‘3 ism jigs ' ' Q PM: ’ ‘ “2‘3ka X} Sigiwmiﬁk him “\"Bmg‘mm Pam; iigivrf} mei§ at; 9g? ﬁ“-~»% l x v G '- “1“” W“ i: ‘This meeﬁ hwswsiesf gin a; : “t gains \ I. ” i a: “a. M \ ﬁgkgggﬂa¥ﬂw 4%” Eﬁve if? in: items. iﬁiw' imhﬁim C “in ice ﬁat 70ming (\$52“? kw {%€§%'® with em Raga} {i-g’ @ﬁﬁeg if? ‘Tkwj; ﬁg i x rd “mg: g rs } h" gﬁﬁwb, 1i i M Li . ' ' ’i w“ V "in u - ‘ i a‘“ L A« is Q} W? ﬁg Mk ﬂing. I . m i Max (b) Find the magnetic ﬂux density at r = 15 cm. (15 points) _ W R U tn; sigh it“; t5 iﬁg hgt'lité ﬁat,“ f“ r? .. r W ESQ alfm W km . «2;. ’ 't m“ mm“ B Ni ‘ -‘ Xian. Urt‘lh égﬂﬁ wgfggéigmjgﬁﬁﬁfﬁ mm taming-“E s .' a“; L r. -‘ M tr“ ms?» t we we E‘s“ mtg, w» lessen Esta wﬁ§%&m% gazﬁa g mar-um ﬁnk-3e; ' ’5 19‘s5 Ewﬁﬁ Mada “a ’QI ﬁgﬁgﬁwf gaging ﬁt a? ) I - as. ‘ 1 khﬂiﬂ" SAKX‘ZJw Wm - “f m e A 1 - 1 t I a taﬁlﬁm‘ﬁ‘ l & Wm w; ‘5” M j; @ {Eagmgg glam? ms new"? t «a? “3“” ‘ ’ A’" \$9“ My“? H 6% * j; T L“, “Millikanmu, “www.mme ‘ (c) A small Wire of length 1 cm carrying current I A in the —2 direction is placed at the point (r r 30 cm, (1) = 0, z = l m). Find the force that results on this small wire. (15 points) “m” Jayme” W am A . may fm “ﬁe-Em ' 3% “ti Jr w ‘ at M as t; “til” “‘33” E: W i a g; at x g gm y: g “26 e g; 5 wail-Egg “My”; ‘M. W “ﬁx tit-N it“? A s it. m. -‘-’ ‘ n f“ “t4 ts t?” a WWW. a j Problem 2 (3 parts: 40 points: A stretchable circular loop of Wire lies in the x-y plane as shown. The loop is expanding in the radial direction at a velocity of 0.1? m/s on all portions of the loop. At time zero, the radius of the loop is 50 cm. A y | Loop is expanding in radial direction at velocity 0.1 m/s (a) If the loop exists in a magnetic ﬂux density 3 = —32 T, ﬁnd the magnitude of the EMF induced in the loop at time zero. (15 points) 33% ft?“ t t m g H *‘ Mhmﬁ gs: Wtﬁmﬁ (b) Do induced currents ﬂow clockwise or counterclockwise in the ﬁgure at time zero? Explain your answer — no credit for unexplained guesses. (10 points) g E Q l E = s is. m: ,' 'é ., ‘ ,- fl '3; 5; ‘ﬁ W% in In; Mémaﬂé vegan e’m EM? gﬁﬁgfmj Kggv gagsf’ 9 r 1’ flash , V we} igﬂkgﬁ‘ WW5); ii" - :9“ "W i "W k é i i V A;- ‘s . a ‘5‘ - ‘2‘ A “1% l %m¢ W glam % We 1 wigs {ng maid? his elite “it; i a I *4“ ' t E“ -- ‘ ‘ it . t ' ‘l‘ é} “em aw _ we gﬁagegi if” M, mg”? giﬁﬁmtaéﬁa g gﬁggg ggégﬁr” ..A q was” 5 (c) This expanding loop is instead placed in the presence of f3 = 2(6r) sin(2r) + 5‘5 cos(2 r) T, where r is the cylindrical coordinate in meters and r is time in seconds. Find the absolute value of the (total) EMF induced in the circuit at time zero. (15 points) Problem 3 5 arts 4 oints each : Circle the best answer. (1) Which of the following is the phasor expression for E = itsin (oat — z) + j;cos(cor + z) ? (d) E = + one” (e) none of the above (2) Which of the following electric ﬁelds would not satisfy Maxwell’s equations in source-free free space? @«t‘i‘ccos [mt —9 V/m .x‘" (b) ﬁcosﬂntiﬂ V/m (c) icos[mt-§ V/m (d) J‘ccos (wt + g) V/m (e) none of the above (3) The displacement current term in Maxwell’s equations: (a) results in a modiﬁed F araday’s Law (b applies to magnetostatic situations @s necessary to ensure consistency with the law of charge conservation ) describes the voltage across an inductor (e) none of the above (4) The inductance of a cylindrical solenoid: (a) decreases as the permeability of the material inside the solenoid is increased (b) will double if the number of turns of wire in the solenoid is doubled (0) increases as the length of the solenoid is increased (keeping the number of turns constant) )(does not depend on the radius of the solenoid LEﬁrone of the above (5)—A boundary exists between free space (2 > 0) and a medium (2: < 0) having a = 480 and n = 2u0 . The ﬁelds in the free space region are E = )“c + 42' (V/m), [’3’ i j; + 22 (A/m) While in the lower region the ﬁelds are E 2 at + 2 (Wm) and 1—7! I 2}“) + :7 (A/m). What is the surface 1 anion the boundary? 3? j (0))? (d) 2 current density .75 ( (a) 0 ‘x (b) (e) none of the above W ...
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ece312_au10_exam1sol - Problem 1 13 parts 40 points A...

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