Final_2003Spring_Solutions

# Final_2003Spring_Solutions - Final Exam Solutions...

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Final Exam Solutions Spring 2003 Some (possibly useful) Relations: enclosed o closed surface Q d ε ⋅= ∫∫ EA G G w closed open path surface d dd dt Es BA G GG G v one turn Nd G G L I closed path dI dL dt G G v 0 closed surface d G G w thru o E closed path E open surface d dI dt where d µµε + Φ Φ= o0 Bs G G G G v 0 2 ˆ 4 µ π × == sr BB 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 / R 22 Joule Heating PI R V QCV = 2 2 1 C 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 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 8.02 Final Exam Spring 2003 PART I (150 points out of 200 points total) DO THIS PART OF THE EXAM FIRST! 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 (20 points) 3 (20 points) 4 (20 points) 5 (20 points) 6 (20 points) 7 (20 points) TOTAL PART I (150 maximum out of 200)
MIT PHYSICS DEPARTMENT ` page 2 Problem 1: Five Conceptual Questions On Material Since 3 rd Exam (30 points out of 200 total point). Circle your choice for the correct answer to the five questions. Question 1 (6 points): The plot above left shows a side view of a capacitor. The plot on the right shows a top view of the lower plate with charge +Q. with electric and magnetic fields E and B at time t . Assume that on the figure to the right above, the electric field is out of the page and uniform over the interior of the capacitor, and that the B field circulates clockwise as viewed from the top. The charge Q is: 1. Increasing in time. 2. Constant in time. 3. Decreasing in time. 4. Can’t tell from the information given. 00 0 Answer: 3 ˆˆ ˆ In cylindrical coordinates ( , , ), the Poynting vector can be written as 11 ˆ () ( ) which points outward. Thus, energy flows out and the charge decreases in time. EB EB Q µµ µ r φ z SE B z φ r G GG = × −= Question 2 (6 points): The B field of a plane electromagnetic wave is given by the expression

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MIT PHYSICS DEPARTMENT ` page 3 ˆ (,) s i n ( ) o yt B ky t ω =+ Bk The electric field of this wave is given by 1.
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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_2003Spring_Solutions - Final Exam Solutions...

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