Final_2005Spring

Final_2005Spring - Physics 8.02 Some (possibly useful)...

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Physics 8.02 Final Exam Spring 2005 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 2005 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 (40 points) 2 (40 points) 3 (40 points) 4 (40 points) 5 (40 points) 6 (40 points) TOTAL
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MIT PHYSICS DEPARTMENT ` page 3 Problem 1: Eight Conceptual Questions (40 points out of 240 total). Circle your choice for the correct answer to the question. Question A (5 points): Consider a cubic volume with sides of length a oriented as shown in the figure. An electric field fills the space both inside and outside the cube and this electric field everywhere points in the +x direction. The magnitude o the field is independent of y and z but varies with x . The value of the electric field at x = 0 is f 2 0 3 ˆ / x o Volts meter a ε = = Ei and the value of the electric field at x = a is 2 0 7 ˆ / x o Volts meter a = = . The total charge contained inside the cube is (a) -10 Coulombs (b) -4 Coulombs (c) 0 Coulombs (d) +4 Coulombs (e) +7 Coulombs (f) Not enough information given to answer Question B (5 points): Consider three equal charges, A, B, and C. Each one sits at the origin ( x = 0 ) but in a different electric potential, as follows: Charge A sits at x = 0 in a potential which is constant and identically zero Charge B sits at x = 0 in a potential which is constant and non zero Charge C sits at x = 0 in a linear potential ( V proportional to x ).
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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_2005Spring - Physics 8.02 Some (possibly useful)...

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