Final_2003Fall_Solutions

Final_2003Fall_Solutions - Physics 8.02 Some(possibly...

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Physics 8.02 Final Exam Solutions 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 A G GG G G v self field self one turn Nd L I BA G G 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 =+ × FE v B G G d Fs B 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 , P q 1 V 4r = = ∆= 22 Joule Heating PI R V / R QCV = 2 2 capacitor 1 Q UC V C =∆ = 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 cT f k = λ= λ = ω 0 1 = × µ SE B G G G 0 1 (,) T x tx t d t T = SS G G 2 0 12 1 sin ( ) 2 T xc t d t T π  =  λ  DOUBLE SLIT: constructive: sin , 0, 1, 2, 3, . .. dm m θ = ±± ± destructive: 1 sin , 0, 1, 2, 3, . .. 2 m θ= + λ = ± ± ± intensity: 2 max cos sin II d π = θ λ SINGLE SLIT: destructive: sin , 1, 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 1 b a dx x ab  

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MIT PHYSICS DEPARTMENT ` page 2 of 18 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 CORRECT 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 CORRECT d) Current clockwise and torque into the page.
MIT PHYSICS DEPARTMENT ` page 3 of 18 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 CORRECT 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 CORRECT d) 0.02 mm

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MIT PHYSICS DEPARTMENT ` page 4 of 18 Question 5 (5 points): A conducting rod moves along conducting rails in a magnetic field that is out of the page. The current in the circuit and the force on the rod are: a) Current clockwise and force to the left b) Current clockwise and force to the right CORRECT c)
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Final_2003Fall_Solutions - Physics 8.02 Some(possibly...

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