FinalExamCoverSheet

FinalExamCoverSheet - Physics 8.02 Final Exam Please Remove...

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Physics 8.02 Final Exam Fall 2007 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = Er G enclosed closed surface o Q d ε ⋅= ∫∫ EA G G w 0 closed surface d BA G G w points from inside to outside d A G moving from to b ab b a a VV V d Δ= = Es G G 2 ˆ 4 o q c r μ π × =< < vr Bv G G G 2 ˆ 4 o I d d r × = sr B G G ˆ where points source observer rf r o mt o sgl loop d d N dt dt Φ = Ed s BdA G GG G v through 0 contour E o d dI dt με Φ ⎛⎞ + ⎜⎟ ⎝⎠ Bs G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d =⋅ JA G G d s is right-handed with respect to d A 2 2 0 1 22 EB o B uE u == () ext q =+ × FE v B GGG G ext d Fs B G 2 cent. Fm v r = IA = μ n G ± τ μ B G z zz dB F dz = VI R L R A ρ = 2 2 ohmic heating V PI V I R R Δ =Δ = = Q C V = Δ 2 2 1 2 2 Q UC V C = B,self,sgl coil N L I Φ = 2 1 2 L UL I = back dI L dt =− 1 C R CX C τ ω = = / L LR X L = = Series RLC: 2 2 00 tan LC ZR X RX X XR V IR ϕ 2 fT k ω =π=π =πλ 1 2 cT f k =λ =ω = με 0l i g h t 0 ˆˆ ˆ Ev B = ×= EB p absorb reflect 0 12 ; SS PP cc = = μ SE B G G G Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆ × = i j k ˆ × = j ki ˆ × = j Some potentially useful integrals:
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