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Exam3_2007Spring_EquationSheet

Exam3_2007Spring_EquationSheet - Physics 8.02 Exam Three...

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Physics 8.02 Exam Three: 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 C V = = 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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