Final_2007Spring_Equations

Final_2007Spring_Equations - Physics 8.02 Some(possibly...

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Physics 8.02 Final Exam: Equation Sheet Some (possibly useful) Relations: Force Laws: ( ) ext ext q = + × F E v B G G G G ext d I d = × F s B G G G Current: ρ = J v G G open surface I d = J a G G Source equations: 2 1 ˆ 4 o dq d r πε = E r G 2 ˆ 4 o q c r µ π × = << v r B v G G G 2 ˆ 4 o I d d r µ π × = s r B G G ˆ points source observer r from to Maxwell’s Equations: inside o closed surface Q d ε = ∫∫ E a G G w 0 closed surface d = ∫∫ B a G G w contour open surface d d d dt = − ∫∫ E r B a G G G G v through 0 contour o o open surface d d I d dt µ µ ε = + ∫∫ B r E a G G G G v Electromotive Force: ( ) d ε = + × E v B r G G G G v Electric Potential Difference: moving from to b a b b a a V V V d = = − E r G G many point charges 1 4 N i i o i q V πε = = r r G G Capacitance: V Q C = 2 2 1 1 ( ) 2 2 Q U C V C = = Resistance: V IR = 2 2 ohmic heating ( ) V P I V I R R = = = Inductance: B,self,sgl coil N L I Φ = back dI L dt ε = − 2 1 2 L U LI =
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Energy Stored in Fields: 2 0 1 2 E u E ε = ; 2 0 2 B B u µ = Energy Flow: 0 1 µ = × S E B G G G ; power surface P d = ∫∫ S a G G AC Circuits: 0 1 LC ω = ; L X L ω = ; 1 C X C ω = ; R X R = Series RLC : ( ) 2 2 2 2 L c Z R X R X X = + = + ; tan ( ) / L C X X R φ = ; 0 0 V I Z = Magnetic Dipoles: =
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