Physics 8.02 Exam Two Mashup Fall 2003 Some (possibly useful) Relations: insideclosedsurfaceoQdκε⋅=∫∫EAGGwpoints from inside to outsidedAGmoving fromtobabbaaVVV∆=−= −∫EsGGd⋅0d−⋅=∫EsGGvmany point charges14NiioiqVπε==−∑rrGGVQC∆=CQV=∆parallelplateoACdε=U = 12C ∆V2= Q22Cseries1211CC=+1Cparallel12CC=+Cwhereis the resistivityρρ=EJGG∆V = i RLRAρ=1Rparallel= 1R1+ 1R2Rseries= R1+ R222ohmic heatingVPi Vi RR∆= ∆==2ˆ4oqcrµπ×=<vrBvGGG<2ˆ4oI ddrµπ×=srBGGˆ pointssourceobserverrfromtothroughcontourodIµ⋅=∫BsGGvwhereIthroughis the current flowing through any open surface bounded by the contour:throughopen surfaceId=⋅∫JAGGds right-handed with respect todA sgl loopddNdtdtεΦ⋅= −⋅= −∫∫E dsB dAvextq=×FvBGGGextdI d=×FsBGGG2cent.Fmv=r= perpendicular to loop,right-handed with respect to I AIμnnG±±=×τμBGGGzzzdBFdzµ=Cross-products of unit vectors: ˆˆˆˆˆˆ0×=×=×=iijjkkˆˆˆ×=ijkˆˆˆ×=jkiˆˆˆ×=kijUseful integrals: 1/ 21/ 22()()dcfcffθθθ=++∫1ln()()dcfcffθθθ=++∫211()()dcffcfθθθ= −++∫Useful Small Argument Approximations (1)1for <<1nnεεε+≅+ln(1)for <<1εεε+≅
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PHYSICS DEPARTMENT Test No. 2FAMILY (last) NAME GIVEN (first) NAMEStudent ID NumberYour Section (check one): ___L01 (Hudson) TTh 12-2 ____L02 (Feld) TTh 2-4 Your Group (e.g. 4A): ______________Instructions: 1. Show all work. All work is to be done in this booklet. 3. This is a closed book test. 4. Calculators and books are not allowed. 5. Do all four problems 6. Print your name on each page of this booklet 7. Crib Sheets are not allowed (Key equations are provided.)Problem Score Grader 1 2 3 4 TOTAL I certify that I have not communicated with anyone about the contents of the 8.02 exam given Thursday evening October 30, 2003 Signed __________________