FinalExam_2008Spring_EquationSheet

FinalExam_2008Spring_EquationSheet - Physics 8.02 Some...

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1 Physics 8.02 Final Exam: Equation Sheet Some (possibly useful) Relations: Force Laws: () ext ext q =+ × FEv B GG G G ext dI d Fs B G G G Current: ρ = Jv G G open surface I d = Ja G G Source equations: 2 1 ˆ 4 o dq d r πε = Er 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 points source observer rf r o mt o Maxwell’s Equations: inside o closed surface Q d ε ⋅= ∫∫ Ea G G w 0 closed surface d = Ba G G w contour open surface d dd dt v through 0 contour oo open surface d d dt μμ Br G G G G v Electromotive Force: ( ) d = +× ⋅ EvB r G G G G v Electric Potential Difference: moving from to b ab b a a VV V d Δ =−= −⋅ G G many point charges 1 4 N i i oi q V = = rr G G Capacitance: V Q C Δ = 2 2 11 22 Q UC V C == Δ Resistance: VI R Δ= 2 2 ohmic heating V PI V I R R Δ =Δ = = Inductance: B,self,sgl coil N L I Φ = back dI L dt =− 2 1 2 L UL I =
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2 Energy Density Stored in Fields: 2 0 1 2 E uE ε = ; 2 0 2 B B u μ = Energy Flow: 0 1 SE B G GG ; power surface Pd = ∫∫ Sa G G AC Circuits: 0 1 LC ω = ; L X L = ; 1 C X C = ; R X R = Series RLC : () 2 22 2 Lc ZR X RX X =+ ; tan ( ) / LC X XR φ = ; 00 VI Z = Magnetic Dipoles: = perpendicular to loop,
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FinalExam_2008Spring_EquationSheet - Physics 8.02 Some...

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