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final_lec2

# final_lec2 - M and speciﬁc heat Cm is dropped mass M of...

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Unformatted text preview: M and speciﬁc heat Cm, is dropped mass M of water but is at the block has come to m mum w W ‘5 With initial temperature Tm, mass t CW 5 3011, WHICH C1150 COHtains 16m mm W” aubrium. W W horblooﬁofmcm’ EL 3 W“ 0M MW from height 1 / W Q’roblem 2 a0 Points). Your ﬁrst engineering job is to design an electric heater that m a battery with internal resistance r. Youneed to choose the value of the heater wire resistance RL so that the battery can deliver the maximum power to the wire. You realize that if RL is zero, no power will be delivered. Also, if RL is inﬁnite there will also be zero power delivered. What is the value of RL (somewhere between 0 and Inﬁnity) that dissipates the maximum power? Prove your answer. (lr‘f) -=>. 1 E I Eur wk“: 8 a—J Y‘ ML “7"ij <”' K‘- .1 do the ﬂ raw-Ma "P EUQL'H‘YZ ' (3'1) ‘4 a 7£.w¢+iw 9% )2,“ ? t/u WI’W of P015.) W J o= \$3.5): (PH-F): (RI.+I‘)--1RL £1 ‘ (Puntnle‘) l r.p,_ A R‘- WMV‘)" (KL-er)“ 5 ‘ (KL-H")! 5 (3N) MIA—‘4‘, ”6am RL=r, pk. PM in MI'WW‘ (’Pr) ( .1 - ,1 / / p4? 5"} ( —- I” 1 ’k —__—_ 41 - D >) AG“ ~f/’(<”\ A. , bl r 1, {a ., Pro U0" '1 f“ ‘ an! e‘ aw {L SMe “> Wit/Mr 57mmei’a\ (P‘Mis at ﬁes 1‘.)th c e a a’llorze Jtﬂ)‘; (a) b) We (”75“ w jE-JZ= 9’5? * . 534;: 11-541 I Problem 5 (15 points) A square metal loop (side length L, mass m, resistance R) is traveling at constant velocity v. It then enters a region with magnetic ﬁeld B. a) What is the force on the wire loop when it ﬁrst enters the region with magnetic ﬁeld? b) What is the force on wire loop once it is completely inside the region with magnetic ﬁeld? c) What is the velocity of the wire loop once it is inside the region with magnetic ﬁeld? d) At what resistance will the loop stop before fully entering the region with magnetic ﬁeld? Is this a maximum resistance or a minimum resistance? It 0. g ,u. v; L‘ 1 *t q<P+cr A4,:L, {1: ya} .. r4 SJV‘ :- ~6 5 JR «“5 00‘5“”! .- A .1381 Problem 6 (15 points). An inﬁnitely long, non-conducting cylinder has thickness r2 — r1. The cylinder has a uniform volume charge density p and is positioned a distance d away from an inﬁnite non-conducting sheet with surface charge density 0. A charged particle (mass m and charge -q) is released from point a, at a height 1 above the cylinder. What is the kinetic energy of the particle when it collides with the cylinder? Neglect gravity. I l I i l p voiume charge density of infinite cylinder :1 surface charge density of inﬁnite piane ﬂ "5 ”4;“ 0" C‘Mé a! ("W-M} 3’439/0/ r {.r ﬁg Mw dF (IL/\Q Cw 9W"; ell/— wilefrnﬂcn / (WY/{:05 we {Mi/r I‘fQ (GUAM, ( [H Aug/J"? Tc / .4 A J “0% 7’4Q cum R we Lf‘cr in J 6‘42» if M/ L” ”J , (All A? VQ ﬂqf ﬂu? P '” HQ {(4 ”Raff ()0. “(0,an “an will “9 \$1,711” A” "" ("Ali‘s/J» «AMA W4 <2 441+“ ”/0 “1‘ ”<4 ‘fﬂr’W’ r“ MC” “131)” (W‘fyslm/a Law» ¢ 1/ H‘.C{*3u\(‘Qf [LC/F r (:K fa“ QQ r4 GV‘Q [LIMK 01(1/ 6Q '2 ’\C,/d 5‘70/ b [/I 6/1"] P tijpf a wCWV Problem 8 (10 points). N electrons per second are shot horizontally into a cavity with a uniform E ﬁeld that points down. (-—-—————-—-——-—————-—————————> a) What must x be relative to L to maximize the B ﬁeld somewhere inside the cavity? L b) What is this maximum value of B and where in the cavity does it occur? gee/f {M ﬂaw. \UV‘IL‘7/L'j . * GI; (92» LCMM'H‘Y 7k Mesa/6+3 M0 pang 75mm pvéu'i‘n} ﬂeet-m (1’16 960%“ Scum/f («v Wit/Q (khaki-\$16 {Le Corned («Me/ital: A/e) @‘Q, q urth‘né {le curred Q): pvt-3):“, ea, 4W5 s:+ «km ...
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