Exam3_EquationSheet

Exam3_EquationSheet - Physics 8.02 Exam Three Please Remove...

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Physics 8.02 Exam Three 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 free, inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G total d d dt dt Φ = Ed s BdA G GG G v 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 0 closed surface d BA G G w 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 parallelplate o A C d = 2 2 1 2 2 Q UC V C = 1 C R CX C τ ω = = B,self,total back dI LL I dt Φ 2 1 2 L UL I = / L LR X L = = Series RLC: 2 2 tan LC ZR X RX X XR ϕ = 2 fT k ω =π=π =πλ 1 2 00 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 If the function Dt satisfies the equation
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