Final_2004Spring

Final_2004Spring - Physics 8.02 Some(possibly useful Relations Final Exam Spring 2004 closed surface E dA = Qenclosed The electric potential at

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Physics 8.02 Final Exam Spring 2004 Some (possibly useful) Relations: enclosed o closed surface Q d ε ⋅= ∫∫ EA G G w total closed open path surface external self open surface d dd dt d d dt ⎡⎤ =− + ⎣⎦ Es B A BB G GG G G v A 0 closed surface d BA G G w closed path thru o E E open surface d d I dt where d µµε Φ= oo Bs G G G G v 2 0 1 2 elec uE 2 0 1 2 mag uB = µ 0 2 ˆ 4 µ π × == sr source source Id d r G q qq =+× FEv G B G B dI d Fs G 0 1 ˆ 4 2 dq r πε = dE r G 2 0 1 ˆ 4 V dq r = Er G 2 1 2 1 P 21 P The electric potential at point P minus that at point P is given by V(P ) d −= G G iN i i1 0i , q 1 V 4r = = ∆= P VI R 22 Joule Heating PI R V / R QCV = 2 2 capacitor 1 Q UC V C =∆= self field self one turn Nd L I G G 2 inductor 1 2 UL = I 0 1 LC = ω 00 1 c = µ ε 1 f T = f T ω= π = π 2 k = πλ cTf k = λ= ω 0 1 = × µ SE G B G G DOUBLE SLIT: constructive: sin , 0, 1, 2, 3, . .. dm m θ= λ = ± ± ± destructive: 1 sin , 0, 2, 3, . . 2 dm m ⎛⎞ + λ = ± ± ± ⎜⎟ ⎝⎠ SINGLE SLIT: destructive: sin , 2, 3, . .. an n θ= λ ± ± Areas, Volumes, etc.: 1) The area of a circle of radius r is π r 2 Its circumference is 2 r 2) The surface area of a sphere of radius r is 4 r 2 . Its volume is 3 3 r 4 3) The area of the sides of a cylinder of radius r and height h is 2 r h. Its volume is r 2 h USEFUL INTEGRALS: d c dx d c () 1 2 d c rdr d c 1 ln d c d dr rc = ⎢⎥ 2 11 d c dr 1 d ⎤⎛ ⎦⎝
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MIT PHYSICS DEPARTMENT ` page 2 8.02 Final Exam Spring 2004 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section (check one): ___MW 10 am ____MW 12 noon ____MW 2 pm ___TTh 10 am ____TTh 12 noon ____TTh 2 pm Your Group (e.g. 10A): _________ Problem Score Grader 1 (30 points) 2 (30 points) 3 (30 points) 4 (25 points) 5 (35 points) 6 (30 points) TOTAL 2
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MIT PHYSICS DEPARTMENT ` page 3 Problem 1: Ten Conceptual Questions. Circle your choice for the correct answer to the ten questions. Question A (3 points): The figure below shows an “iron filings” representation of the field of a magnetic dipole plus a constant field. The constant field points to the upper right corner of the image. If the magnetic dipole is free to rotate, then the dipole will a) Not rotate since the torque on the dipole is zero in a uniform field b) Rotate clockwise c) Rotate counterclockwise d) Impossible to tell without more information Question B (3 points): In the circuits below, all of the batteries and light bulbs are identical. A B C Let the light put out by the top bulb in each of the above circuits be A P , , and , respectively. Then B P C P a) A BC PPP == b) A >= c) A <= d) BA C C B e) f) CA < = g) B h) A < < 3
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MIT PHYSICS DEPARTMENT ` page 2 Question C (3 points): Five loops are formed of lengths of identical cooper wire. Loops 1, 2, 3 and 4 have exactly the same dimensions; loop 5 has the same height as the others but is longer. At the instant shown in the figure, all the loops are moving at the same speed in the directions indicated. There is a uniform magnetic field pointing out of the page in region I; in region II there is no magnetic field. Ignore any interactions between the loops.
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This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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Final_2004Spring - Physics 8.02 Some(possibly useful Relations Final Exam Spring 2004 closed surface E dA = Qenclosed The electric potential at

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