Exam2_2007FACover

Exam2_2007FACover - Physics 8.02 Exam Two Fall 2007 Please...

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Physics 8.02 Exam Two Fall 2007 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: inside, free closedsurface o d κ ε ⋅= ∫∫ EA w Q G G d A G b d G points from inside to outside moving from to ab b a a VV V Δ= = Es G many point charges 1 4 N i q V = i oi πε = rr GG V Q C Δ = C V = Δ Q U = 1 2 C Δ V 2 = 2 Q 2 C series 1 2 CC =+ 11 1 C ; parallel 1 2 C Δ V = i R L R A ρ = series 1 2 parallel 1 2 1 ; R RR R 2 2 V Pi V i R ohmic heating R Δ =Δ = = 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 points source observer rf r o mt o through contour o dI Bs G G v where through open surface I d =⋅ ∫∫ JA G G d s right-handed with respect to d A sgl loop d d N dt dt Φ = Ed s BdA G G v 2 2 0 1 22 EB o B uE u == B,self,total back dI LL I dt Φ 2 1 2 L UL = I ext q Fv B G G G ext d Fs B G 2 cent. Fm v = r = perpendicular to loop, right-handed with respect to IA I μ nn G ± ±
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