MTE : Ch 13 5:3-7pm on Oct 31 ltenate Exams: Wed Ch 13 6:3pm-8:pm (people attending the altenate exam will not be allowed to go out of the oom while othes fom pevious exam ae still aound) Thu @ 9:-1:3 am Thu @ 6:3pm-8:pm in the lab Ch 354 You have eceived an email saying that you equest fo an altenate exam was appoved. f you did not, please notify me at the ed of this lectue eview MTE P8 Contents of MTE Electic Potential and Field Capacitos and capacitance Cuent and esistance, Ohm s law DC Cicuits and Kichoff s laws C cicuits Electic potential enegy Wok is Foce x distance (taking into account cos between vectos) W hand = "U Loentz foce and motion of chage in a magnetic field iot and Savat mpee s law (MTE3, so study it) ead chaptes 8 (no 8.)-9-3-31-3 > since they epel potential enegy inceases f opposte chages they attact => W < and potential enegy deceases 4 Example E Potential Electic Potential q q& V = k% " ( = $ d d' Calculate the electic potential at y Calculate the electic potential at x d -1 µc d=4 m - +1 µc + d1=3 m 3m 3m q q & q V = k% " (=k 3d1 $ d1 3d1 ' Q souce of the electic potential, q expeiences it Calculate the wok YOU must do to move a Q=+5 mc chage fom to. WYou = "U = U U = Q(V V ) = k 5 qq 3d1 6
Wok and electostatic potential enegy Question: How much wok would it take YOU to assemble 3 negative chages?. W = +19.8 mj. W = -19.8 mj C. = Likes epel, so YOU will still do positive wok q W 1 = 3 3µ W = k q 1q = 9 "1 9 1"16 " "1 6 = 3.6mJ 1 5 5 m 5 m W 3 = k q q 1 3 + k q q 3 =16.mJ 13 3 q q 1 W tot = k q 1q + k q 1q 3 + k q q 3 = +19.8mJ 1µ µ 1 13 3 5 m U E =19.8mJ electic potential enegy of the system inceases 7 Electic Potential and Field Points at m and at 5m on the x axis ae in a egion whee the electic field is unifom and given by E = 4i+3j N/C. What is the potential diffeence V - V? ) -1V ) +1V C) -4V D) +4V (,) (5,) E = 4i N/C E = "V $ E x = " dv dx $ dv % = "E x % dx $ V "V = 4 & 3 =1V x(m) 8 emembe Capacitos Capacitance of a capacito: Paallel plate capacito: Enegy stoed in a capacito: C = Q "V Depends on geomety and mateial between plates U = Q C = 1 C"V = 1 Q"V Enegy stoed in a paallel plate capacito The paallel plates of an isolated capacito with vacuum between them ae given equal and opposite chage. f the plates ae pulled fom a distance d to D > d, does the enegy stoed in the capacito ) 1) ncease ) ) Decease C) 3) emain equal q is the same E is the same = q/() "V inceases = Ed C deceases U inceases q is the same because C isolated U = q C C ini = " d C fin = " D $ C fin < C ini $ U fin > U ini 1 Capacitos in paallel and seies "V1 = "V = "V Qtotal = Q1 + Q Ceq = C1 + C Q1=Q =Q "V = "V1+"V 1/Ceq = 1/C1 + 1/C Calculate the equivalent Capacitance C 1 = 1 µf C = µf C 3 = 3 µf 1 = 1 1 + + 1 " C eq = 6.9µF C eq C 1 C + C 3 C 4 C 4 = 4 µf V = 5 Volts C 1 C V C 3 V = V 1 + V 3 + V 4 V 3 = V = V 3 Q = Q 1 = Q 3 = Q 4 Q 3 = Q + Q 3 V = Q = Q Q + + Q C eq C 1 C + C 3 C 4 C 4 paallel C 1, C 3, C 4 in seies 11 1
Electic cuent veage cuent: nstantaneous value: S unit: ampee 1 = 1 C / s n = numbe of electons/volume n x L electons tavel distance L = vd "t av = %Q/ %t = nel v d /L Cuent density J= / = nqv d (diection of + chage caies) Ohm s Law: %V = (J = & E o E = $ J) %V = EL and E = ' J => ' / = %V/L = $L/ esistance in ohms (") L =1V =1 V Equivalent esistance 1 = = k" = 3 = eq =3/ = 3 k" Which is the coect equivalent cicuit? ) ) =1V eq =3 = 6 k" Quiz on a simple DC cicuit dentical Light ulbs in paallel and seies =1 V 1 = = k" =1V 1 == k" ) ) P = = " 4 = " 4 ) P = 4 = " 3 = = eq = eq + 1 = 3/=3 k" =1V eq = 3 k" eq =/ 1 eq = 1 + 1 = " eq = Light ulbs in seies: which is moe luminous? ) ) ) and ) have the same luminosity n which of the cases the bulbs will be moe luminous? - paallel - seies ) Light ulbs in paallel: which is moe luminous? ) ) / / =/ ) and ) have the same luminosity gain powe dissipated in esistos Kichhoff s ules Junction ule: $ in = $ out statement of Consevation of Chage 1 = + 3 Loop ule: "V loop = "V k = k statement of Consevation of Enegy The banch with and has lage esistance than the one with C so less cuent flows in it 17
Kichoff s laws application 1 3 loops ssume 1 cuent vese pe loop Enegy balance in a cicuit 1 Chemical enegy povided by batteies is dissipated in esistos (Joule heating) UT take into account the vese of batteies and cuents flowing in esistos (given this you can conside 1 cuent pe loop 1 and and emembe that in the banch in common between the loops te cuent is 1-) 1 = + 3 " 3 = 1 8V + 4V 4V 1$ 1 $ 1 $( 1 ) = 4V $( 1 ) 6$ = 19 P =1" 1 + " 1 + "( 1 ) + 6" P $ = 8V % 1 + 4V % 1 4V % ( 1 ) Powe = ate of enegy loss P = "U = "Q "t "t "V P = "V = = "V Light bulbs and capacito C Cicuits The cicuit below contains 3 identical light bulbs and a fully chaged capacito. Which light bulb(s) is (ae) bightest? What is the value of the time constant of this cicuit? ) 6 ms ) 1 ms C) 5 ms equivalent cicuit 1 C Cicuits: CHGE/dischage OF C S 1 C " = dq dt + q C q(t) = C"(1 e t / C ) (t) = " / C et =1", C=3 mf and = Volts = " dq dt = q C "t / C q(t) = q e (t) = q C e"t / C S 1 U dissipated = (t) $ dt = $ e "t / C dt = = q C C = q C C Loentz foce and H ule n electon moves in the plane of this pape towad the top of the page. magnetic field is also in the plane of the page and diected towad the ight. The diection of the magnetic foce on the electon is () towad the top of the page () into the page (C) towad the ight edge of the page (D) out of the page This is the enegy stoed in C 1/9/ U. Wisconsin, Physics 8, Fall 6 4 F v 3
Quiz on Motion of a chaged paticle in chaged paticle taveling in the plane of this sceen entes the egion of a unifom magnetic field pointing into the sceen, as shown. The subsequent path of the paticle in the egion of the magnetic field could be epesented by: Centipetal foce defines the cicula tajectoy and points to the cente of the cicle. ) Path 1 ) Path C) Path 3 D) ll of them Magnetic Foce on wie with a Cuent and between wies Foce on each chage Foce on length ds of wie F = L " qv " qv " ds df = ds " ttactive fo paallel cuents. epulsive fo antipaallel cuents foce/length s it a positive o a negative chage? 1/9/ U. Wisconsin, Physics 8, Fall 6 5 F /L = µ 1 4" a 6 magnetic dipole moment: Foce on a wie and toque on a loop with cuent µ = vecto diection: ( to plane of the loop in the diection the thumb of ight hand points if finges cul in diection of cuent. Toque on loop Stable equilibium when U = " µ = "µ µ ) = sin* and o plane of loop pependicula to diection of * 7 x w F F *. µ Foce ) couple µ n which of these cases the magnitude of the toque is lagest? () a () b (C) c a nothe on Toque b µ " " µ nswe: (c). all loops enclose same aea and cay same cuent + magnitude of µ is the same fo all. (c) µ upwads, µ ( and " = µ. (a), ) = (b) ) = µsin* 1/9/ U. Wisconsin, Physics 8, Fall 6 8 c iot-savat Law Fo a single chage in motion = µ qv u 4" Fo a wie with cuent out of page * ds d = µ o ds ˆ 4" qv " ds Each element of cuent poduces a contibution to the magnetic field. 9 Question on iot-savat s Law i d How is the -field diected fo a wie with a cuent flowing out of the page at a distance fom the wie? Field lines ae tangent to the cicle of adius = µ 4" i dl = µ 4" i " = µ i What if thee ae wies? -field supeimposes -= i i = µ i 3 + µ i = 4µ i 3 1/9/ U. Wisconsin, Physics 8, Fall 6 3
Moe Questions What if the poblem is bi-dimensional? Points at (,3)m and at (5,7)m ae in a egion whee the electic field is unifom and given by E = 4i+3j N/C. What is the potential diffeence V - V? y (m) (5,7) Text (,3) E = 4i+3j N/C E = "V $ % dv = " % E& ds = 5 7 " % 4dx " % 3dy = "1 "1 = "4V $ V "V = 4V 3 x(m) 1/9/ U. Wisconsin, Physics 8, Fall 6 31 3 Electostatic Potential of like chages Toque on a loop with cuent loop of cuent-caying wie is initially aligned with its plane in the diection of a unifom magnetic field. What happens to it? ) ) C) Electostatic potential V () = k Q (point chage Q) V = k Q,V = k Q U = k qq,u = k qq Potential depends on souce chage and on distance, and it is independent on the test chage. 33. Stays paallel to magnetic field. otates till it is pependicula to field C. otates continuously Toque aligns loop (, 34