1e3test2-2004-solutions - PHYSICS 1E03 TEST Name 3.25 Mg...

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Unformatted text preview: PHYSICS 1E03 TEST Name 3.25 Mg .- Student Number March 16, 2004 Instructors: K. Sills (section C01) N. McKay (sections C02, C03) D. Venus (section CO4) W. Harris (section C05) Instructor: Lecture Section: Write your name and student number on your paper before you begin. Multiple-choice questions are worth 2 marks each (only the answer is marked), and problems are worth 3 marks each (clear solutions required). Only the McMaster standard calculator (Casio far-99]) is allowed. Notes and formula sheets are not permitted. Some formulae are given below; if you use them it is your responsibility to know what they mean and when they can be used. Earth’s gravitational field: 3 = 9.81 111st Electron mass: m, = 9.11x10‘3‘ kg Electronic charge: 8 = 1.50x1tr‘9 C Proton mass: mp = 1.67x10‘27 kg Permeability of vacuum: 110 = 4mm“? Tina-A"1 Coulomb’s Law constant: k - : ' '><109 N-mzr'C2 Pernu‘rtivity of vacuum: gassmo—u GEN—Ema -—r a mi ) I F: E CE—— 6’ J:——: v :01? R. :R +R +... q AV . A "Gd series 1 2 A _ RA _ _ u F=qn (3:chE pack? Rpalmngl=R1I+R21+w F=qE U :écv2 V=IR Cpmtu =61 +C2+--- E=ke-%-f P=IV Claim: =C1‘1+C2“+-.- l" l _ - q’E =§E.dA=€_Q3“C =47d€eQenc g(f)=QD€ f/RC' q(I)=Qfinal (1—6 (IRE) 0 plane: Ezi=27wed F=qv><B dB:£9_Ids><r 250 43 r3 conductor: E=£=4zzkea F=IL><B fB'dS=#oIencichcd go _ —_ * *_~ “ » < _fl01 U—ql/ r—I xB—pr stra1ghtw1re, B— 2rrr V=k,,£ F=ma solenoid, Bacon} 1. 1’2 2 (fl/:fl-Ecds a, =—— K=-]2—mv ,. 1—9 10 1 1 12 Total (18) (3) (3) (3) (30) continued on page 2. .. Page 2 of 8 pages Part A (multiple choice): Print the letter corresponding to the best or most nearly correct answer in the box beside each question. Each correct answer is worth 2 marks. 1. The two capacitors shown have the same initial charge Q. The switch is then closed. Once the charges stop moving, what is the final charge on the positive plate of the lttF capacitor? A) zero B) %Q RHSWBT e #2 2. A capacitor constructed from two parallel metal plates with a dielectric (dielectric constant = 2) in the gap between them. The plates are connected to a battery, and remain connected as the dielectric is removed from the gap. As the dielectric is being removed, the charge on the positive capacitor plate 3 -- ains constant C) increases D) changes from to positive to negative 3. A large capacitor is charged with a 9-volt battery. When the battery is disconnected, and a screwdriver blade is then placed across the capacitor terminals, sparks fly and the blade welds to the terminals. The capacitor can do this because A) it prevides much more charge than the battery B) it provides much more current than the battery C) it multiplies the battery voltage by a large factor D) all of the above 21118“! er continued on next page. .. ~ Page 3 of 8 pages 4. The resistance between the ends of a rectangular strip of thin aluminum foil 200 cm long and 20 cm wide is 0.4 ohms. The resistance of a piece of the same foil half as long and half as wide would be answer : 0.0 . QC: /2() _|__./ C) 0.05A I“; D) 0.5A 20g}: 69 answer ___l_/__ F6 ,4 J-£-F_flE/ZC_Olol_—Z4 6. Four identical capacitors, each of capacitance C, are arranged in a network as shown. If the equivalent capacitance, between points A and B, is 9.0 p: F, what is the capacitance C of a single capacitor? A) 30y}: c B) 6.8,uF ’ ’1 d | ii | c) 9.0i 81%“ EC- 4 (36} l A C H fl (3 C b 73:5 c.= 26% continued on next page. .. Page 4 of 8 pages 7. A long straight horizontal wire carries a current I as shown. An electron directly above the wire is accelerated to the left by the magnetic force due to the wire. This is possible if .2") 3 A) the electron was initially moving in the +y direction a ‘v [2 (Mo/l 2’ B) the electron was initially m0ving in the -y direction ‘— Q i? C) the electron was initially m0ving in the +2: direction 3’ D) the electron was initially moving in the +2 direction I x answer (3 our ofpage} 9 at 8. A single circular loop of wire in the x—y plane carries a current I as shown. The Jeep sits in a uniform magnetic field B pointing in the H: direction. The torque exerted on the loop by the field is a vector o the y axi‘ B) parallel t 5. m - o I e z. axis (perpendicular to the page) D) none of the above B answer A A x . :3 {B / [A P) £7 9. Two identical bar magnets are placed as shown. What is the direction of the-tog agnetic field they create at point P? - f \. , ’m' ® El ['lSW'Cl' C continued on next page. .. Page 5 of 8 pages Part B (Problems): Write a clear solution showing how the answer is obtained. Each problem is I3 4 worth 3 marks. 2 Q 10. Calculate the current I1. 0);; Irrltsmw.) (0-170 {QM}. \‘z\) -'(._.25?3 I. ‘lOflLL :0 may) CadeC'. (ponBLgCIzg-Ifliywzo '5 "flgr + ){waéwfi} @ [email protected]@: 6T9— 11/4 If 137+ answer ,7} 7 /€; ’4 continued on next page. .. Page 6 of 8 pages '1 I , Sin gly-cllarged ions (lql=e) are accelerated from rest through a MOO-volt potential difference, and then enter a uniform magnetic field B = 3.0 T, moving perpendicular to B. In the field, the ions move in a semicircle of diameter 20 mm. Calculate the mass of one of the ions. 2;. lg, g0 iBrf mizél/xt 1M W answer 2:7 5/ 20”“ $7 continued on next page. .. Page 3’ of 8 pages 12. Current I] is flowing along an infinitely long straight vertical wire. Current. 12 is flowing along around a small square loop beside it, as shown. Calculate the net magnetic force (magnitude and direction) on the square loop, in terms of the currents and the distance a on the diagram. Show the details of the derivation of your result, with briel‘ explanations. continued on next page. .. Page 8 of 8 pages 13. Current I flows up a long vertical wire, around a circular are of radius a, and out a long horizontal wire as shown. Use the Biot-Savart Law, B _ J- #0] ds Xi‘- _ 47: r2 to derive an expression for the field E at point P, in terms of a, pig, and I . Show clearly the vectors d§ and P on a diagram. and justify, with a brief explanation, each simplifying step in evaluating the integral. Give the direction of E as well as its magnitude. I ...
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