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# q9 - PHYSICS 2B(a QUIZ 9 SPRING QUARTER 2001 PROF SCHULLER...

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Unformatted text preview: PHYSICS 2B(a) QUIZ 9 SPRING QUARTER 2001 PROF. SCHULLER JUNE 1, 2001 USEFUL FORMULAS: a 1 A _ Coulomb' 3 Law F = Q1212 r For a capacxtor 471780 r CV = 8Q Gauss’ 8 Law éE-d (i=8 —J p dV C: d A(Parallel Plate) P_. — . , Definition of Potential V: JE- dl U = 1 l qqu Electrostatic Energ)l 47180 2 ”q rij 80:8.9X10711 C7 Rsz R=m Nm* A qB E: W V = R1 RC Circuits , Charging , D15Chdf§lllg_ W F = qv X B F = iL x B rzyxB a — « _ , ,uoi ~ 0 .dlx? :ﬁB-dl zpdlds Ampereslaw B(r)=— dB=—— 1 g x 2m 47r r = jB - (IA 8 = N d¢B dt 1. A rectangular loop of wire of dimensions 1 and (d-2a) lies in the plane of two very long. parallel wires, which comprise part of a circuit (see figure below). Calculate the mutual inductance between the loops. PHYSICS 2B(a) QUIZ 9 SPRING QUARTER 2001 PROF. SCHULLER JUNE 1, 2001 2. In the circuit shown in the ﬁgure below, 8 = 10 V, R1 = 5.0 9, R2 = 10 Q, and L = 5.0 H. For the two separate conditions (I) switch S just closed and (II) switch S closed for a long time, calculate (a) the current il through R1, (b) the current i2 through R2, (0) the current 1' through the switch, ((1) the potential difference across R2, (6) the potential difference across L, and (f) the rate of change diz/dt. 3. In the ﬁgure below, a conducting rod of mass m and length L slides without friction on two long horizontal rails. A uniform magnetic ﬁeld B fills the region in which the rod is free to move. The generator G supplies a constant current i directed as shown. (a) Find the velocity of the rod as a function of time, assuming it to be at rest at t = 0. The generator is now replaced by a battery that supplies a constant emf 8. (b) Show that the velocity of the rod now approaches a constant terminal value V and give its magnitude and direction. (c) What is the current in the rod when this terminal velocity is reached? (d) Analyze this situation and that with the generator from the point of View of energy transfers. 4. (BONUS) The Germans, English and French contributed greatly to the development of electricity and magnetism. Name for two of these nationalities: (a) a famous physicist (b) a good dish 6’) genus ‘ NVIHuO“ QuylL‘nhi" here nse‘cs \[av SP+5 /C0‘ll/1 3S “ne 2 lomﬁ wires. 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SCHULLER JUNE 1, 2001 USEFUL Fg IRMIJLAS: a 1 A . Coulomb's Law F = (11:12 r For a capac1tor 47:80 r CV=Q , ~ ~ 1 80A Gauss 5 Law §E - dA = —— f p dV c = —d— (Parallel Plate) S 80 V . . . . P ~ -’ 1 1 qiq j . Deflnltlon of Potentlal V :1 E ~ d1 U —— —— Electrostatlc Energy °° 471's0 2 ”.1- r1] 2 e(,=23.9><10—12 C, R=p£ R 3‘1 Nm A qB RC Circuits Charging Discharging F = qv X B (e/R)e“"RC) - (Q0 /RC)e(“/RC) r = [J x B §Edl=pOII~d§ Ampere'slaw B(r)=& dlﬂ3=ﬂ°—idl:<r s 2m 47: r 61¢ = BdA ts=N——B «a. I dt 1. A metal rod is forced to move with constant velocity V along two parallel metal rails, connected with a strip of metal at one end, as shown in the figure below. A magnetic ﬁeld B = 0.350 T points out of the page. (a) If the rails are separated by 25.0 cm and the speed of the rod is 55.0 cm/s, what emf is generated? (b) If the rod has a resistance of 18.0 (2 and the rails and connector have negligible resistance, what is the current in the rod? (c) At what rate is energy being transferred to thermal energy? 2. In the ﬁgure below, 8 = 100 V, R1 = 10.0 9., R2 = 20.0 Q, R3 = 30.0 (2 and L = 2.00 H. Find the values of i1 and i2 (a) immediately after the closing of the switch S, (b) a long time later, (c) immediately after the reopening of switch S, and (d) a long time after the reopening. PHYSICS 2B (b) QUIZ 9 SPRING QUARTER 2001 PROF. SCHULLER JUNE 1, 2001 3. A large, closely packed coil of N2 turns completely surrounds a very long, ideal solenoid of length l, radius a, and N, turns, as in the ﬁgure below. Calculate the mutual inductance M between the coils. 4. (BONUS) The Germans, English and French contributed greatly to the development of electricity and magnetism. Name for two of these nationalities: (a) a famous physicist (b) a good dish Q7 : 0.357— L= <2.st v2 O‘SSM/S R= |3_rL g .5 if: M Lx ELI; m V = (osSXOJSXoss) “ _€__ 0,04%! _‘ -3 I (a) ‘- R T“ 2.Q7xtoA (SP—M.) .1 'Z “4 C) P: ‘K= (2.cqx(ds)(\%3= (S Ids) [I f“ K3 2 -. 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