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Test 4 Fall 2009 - PHYS 2212 Test 4 November 18th 2009...

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Unformatted text preview: PHYS 2212, Test 4, November 18th, 2009 Name (print) ______£§%_:__Q_é ________________________________________________________________ Instructions 0 Read all problems carefully before attempting to solve them. 0 Your work must be legible, and the organization must be Clear. 0 You must show all work, including correct vector notation. 0 Correct answers Without adequate explanation will be counted wrong. 0 Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything you don’t want us to read! 0 Make explanations correct but brief. You do not need to write a lot of prose. 0 Include diagrams! a Show what goes into a calculation, not just the final number, e.g.: g = W = 5 x 104 0 Give standard SI units with your results. Unless specifically asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you can’t calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge “In accordance with the Georgia Tech Honor Code, I have neither given nor received unauthorized aid on this test.” Sign your name on the line above The PHYSICS 2212 FINAL EXAM will be: Dec 8th from 2:50pm - 5:40pm Please read the announcement on WebAssign. Problem 1 (25 Points) At a particular instant, an antiproton (a particle with the mass of the proton, and charge ——e) is traveling with velocity (2.5 X 105,0,O> m/s. In this region there is a uniform electric field of (1.5 X 104, 0,0) N/C, due to charged plates not shown in the diagram, and a uniform magnetic field of (0, O, —0.03) T, due to large current—carrying coils not shown in the diagram. (a l7pts) Calculate the net force on the antiproton at this instant, neglecting the effects of the Earth’s magnetic and gravitational fields. Your answer should be a vector. Clearly show all steps in your work. .__> —‘>; ”‘>’ fi+:F€—TFB E: CEE‘: ’(i'iaWO’mC a - a: éQ-‘i‘lo ‘s/o/ O>M .2; l; )<l.§.po4, o, o) ”/c, .9 .3, Q " Q '~— — ‘1 ‘F ” VXB ‘1 __ L910 WC> ., ‘7’ fi ( 25.1035 0 o 0 o -0.03T —5> ’ g ' F8 '— < O —-()«lg'lcfw’d(Ls-(0“L wt/s)( 003 T3 ) o5 ’ ) A - "’5’ ’PB : <ol-I.Z'/0 ,0) IJ A, A -15 fir: <-2»’-f'(0"{,‘/.2 «(o , o> (b 8ptS) On the diagram, W two arrows: one representing the magnetic force and the other representing the electric force that you calculated in part (a). Make sure your arrows agree with your answer to part (a). That is, the relative length of your arrows should correspond to vector magnitudes. Problem 2 (25 Points) A large disk-shaped plate of plastic of radius 2 m has a charge of ~5 x 10‘8 coulombs distributed uniformly over its surface. The center of a solenoid, of length L = 2 m and composed of N = 3000 turns of wire, is located 0.5 cm from the charged plate. At a particular instant a proton is inside the solenoid, traveling along the 3: axis with velocity 17 =< —3 X 104, 0, 0 > m/s. For a solenoid, the magnetic field inside is uniform everywhere, parallel NI to the axis and given by: B m MOT. (a l6pts) Determine how much current I must be run through the solenoid to keep the proton from being deflectedgoward fie cliaiged disk. )5 ._>,. .2 — p17 X‘B)’ fiat: EtF-B:<o,o)05 :5 Ft'FB M E, ‘ ._>> q ~3, '~§ ' X7/C filg, leB':l\/“B I“ E=vB , IQ L [ell/A MONI T: zéo : V ’ L ’3 ' zero/UM ./- \ y (b 9pts) The figure on the left shows the solenoid and plate when viewed from above (the positive y-axis). On this figure draw: the direction of current flow in the solenoid, the direction of the force on the proton due to the solenoid and the direction of the force on the proton due to the charged plate. Vector lengths must be scaled to correspond to the relative magnitude of the vectors. Problem 3 (25 Points) Voltmcz‘cr A bar (L = 18 cm, h = 5.2 cm and d = 2.1 mm) made of a conducting material is connected in series to a power supply with emf 2 +115 volts. A voltmeter is attached ver- tically across the bar, with the leads directly opposite each other, and reads +2.8 X 10—5 V, Large coils not shown in the diagram cre- ate a magnetic field of 0.7 tesla in the +z direction. A voltmeter gives a positive reading if the negative lead (COM) is connected to the lower potential location, and the positive lead is connected to the higher potential location. (a 3pts) What is the direction of E“, the electric field inside the bar due to charges on the surface of the wire, and in and / or on the power supply? Briefly explain how you know this. ~76 b/c MM ml at m Lam cs fl'l" l/liallutr (Jake/tidal. (b 3pts) What is the sign of the mobile charges in the bar? Briefly explain how you know this. ~H/LL VDH’M‘l-(«r Mtg; (war—five ) CCi’lv-L VIC virtue, lot/oar .2ch 0?- M bar (‘5 W 0dr hiqlrcf (>5ka 0“ ("F Chances cellecl Wm), rte 0“ wlodw'v-e— charges (‘5 ”P (c 3pts) What is the direction of the drift velocity of the mobile charges? +x 5&4 Pow-i (0L) 0r (‘0) (d 3pts) What is the direction of the magnetic force on the mobile charges? Briefly explain how you know this. .2 _—> «1 W +1 372MB (e 3pts) What is the direction of El, the transverse (or perpendicular) electric field due to the magnetic polarization of the bar? +3 fasi‘HN chawfies 6w loa‘l’fiiom cl: bar, Nch‘Hk/LQ Chou/“0‘9. Cavri~cv5 (Okleci' cm 42>? (f 6pts) What is the drift speed of the mobile charges? Show all steps in your work. my“) 7&5vzaw V43=EL= 7:- VA: 53!. ML... : 947.!0' “4/5 Eh ' (0‘77“)(5’2‘10V2M) (g 4pts) There are 4 X 1024 mobile charges per cubic meter of this material. The absolute value of the charge of one mobile charge is +6. What is the value of the conventional current in the circuit? Show all steps in your work. jrzm/lvd T (/ Q'lo‘lc’c)(‘/'/0?4 “7.3) (9240’V")(7~"/0ym)(3“""/04/'%l j : 36.84%0’2A Problem 4 (25 Points) An infinitely long, solid plastic cylinder (radius R) has negative charge distributed uniformly everywhere in the cylinder’s volume. Any section of the cylinder with radius R and length L contains a total negative charge —q. By symmetry, the electric field points radially inward at all locations outside, on and inside the cylinder. (a 9pts) On the diagram below, draw the electric field vectors at locations A, B and C. Gauéfiiflw Cami” 0P Lac-1W /£ \ Cc\\\‘mlev uni-W (aches a “LIA Q/QMa‘x-V L , Cuwl—m'ws: (Marie 1%?) (b 16pts) Determine the electric field at location C inside the cylinder, a distance d radially from the symmetry axis of the cylinder. Explain in detail, including all assumptions, directions, calculations, etc. (PM : 28M Ci>ev1d5 =0 We E J, 3 WW “Q5 60 Z Troll/L (2m W'— . .3; ../~ -; ————"" K. «ad—lo oi: 4211+ 7 § ENI/ldm : Elfidfl ) éo 6° 4w Volt/«MS ...
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