Final_2003Fall

# Final_2003Fall - Physics 8.02 Some (possibly useful)...

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Physics 8.02 Final Exam Fall 2003 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 self field self one turn Nd BA G G L I 2 inductor 1 2 UL = I 0 closed surface d G G w thru closed path oE E open surface dI d dt where d µ µε + Φ= o o Bs G G G G v 0 2 ˆ 4 π × == sr source source Id d r G q qq =+× FEv B B G G d Fs G 0 ˆ 1 4 2 dq r πε = r dE G 2 0 1 ˆ 4 V dq r = Er G b a VV ( b )V ( a ) d ∆≡ = − ⋅ G G iN i i1 0i , q 1 V 4r = = ∆= P 22 Joule Heating PI R V / R QCV = 2 2 capacitor 1 2 Q UC V C =∆= 2 0 1 LC = ω 2 0 1 2 elec uE = ε 2 0 1 2 mag uB = µ 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 0 1 (,) T x tx T = SS t d t G G 2 0 12 sin ( ) 2 T xc t d t T π ⎛⎞ 1 = ⎜⎟ λ ⎝⎠ DOUBLE SLIT: constructive: sin , 0, 1, 2, 3, . .. dm m θ = ±± ± destructive: 1 sin , 0, 2, 3, . .. 2 dm m θ= + λ = ± ± ± intensity: 2 max cos sin II d π = θ λ SINGLE SLIT: destructive: sin , 2, 3, . .. an n θ= λ ± ± intensity: 2 max sin sin sin a a ⎛π θ λ = π θ λ USEFUL INTEGRALS: b a dx b a () 1 2 b a x dx b a 1 ln b a b dx x a = ⎢⎥ 2 11 b a dx 1 x ab ⎤⎛ ⎦⎝

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MIT PHYSICS DEPARTMENT ` page 1 of 17 8.02 Final Exam Fall 1803 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section (check one): ___L01 (Hudson) TTh 12-2 ____L02 (Feld) TTh 2-4 Your Group (e.g. 10A): __________ Problem Score Grader 1 (30 points) 2 (30 points) 3 (30 points) 4 (30 points) 5 (30 points) 6 (30 points) TOTAL
MIT PHYSICS DEPARTMENT ` page 2 of 17 Problem 1: Six Conceptual Questions. Circle your choice for the correct answer to the six questions. Question 1 (5 points): In the circuit above, we have an initially uncharged capacitor and two identical resistors. Neglect any inductance in the circuit. At the instant the switch is closed, a) 0 CR II == b) / I IR ε c) 0 / 2 I d) / 0 I e) / / 2 I RI R Question 2 (5 points): A square coil rotates in a magnetic field directed to the right. At the time shown, the current in the square, when looking down from the top of the wire loop, and the magnetic torque on the loop, will be: a) Current counterclockwise and torque out of the page b) Current counterclockwise and torque into the page c) Current clockwise and torque out of the page d) Current clockwise and torque into the page.

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MIT PHYSICS DEPARTMENT ` page 3 of 17 Question 3 (5 points): A coherent monochromatic spherical wave impinges on two apertures separated by a distance d. An approximate formula for the path difference between the two rays shown is a) sin L θ b) cos L c) cos d d) sin d Question 4 (5 points): A laser beam produces red light of wavelength 600 nm. That light impinges on two long narrow apertures (slits) that are separated by a distance d . Each aperture has width a , with a << d . The resulting pattern on a screen 10 meters away from the slits is shown above. The width a of the slits is a) 0.03 mm b) 0.06 mm c) 0.01 mm d) 0.02 mm
MIT PHYSICS DEPARTMENT ` page 4 of 17 Question 5 (5 points):

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## This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Final_2003Fall - Physics 8.02 Some (possibly useful)...

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