Final_2006Fall_Solutions

# Final_2006Fall_Solutions - Physics 8.02 Final Exam Equation...

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Physics 8.02 Final Exam: Equation Sheet Fall 2006 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 closedsurface o Q d κ ε ⋅= ∫∫ Ea G G w 0 closed surface d = Ba G G w B d dt Φ =− through 0 contour oo open surface d d dt µµε Br G G G G v Electromotive Force: ( ) d = +× ⋅ EvB r G G G G v Magnetic and Electric Flux: B open surface d Φ≡ G G E open surface d Φ ≡⋅ G G Electric Potential Difference: moving from to b ab b a a VV V d =−= −⋅ G G many point charges 1 4 N i i oi q V = = rr G G Capacitance: V Q C = 2 2 11 22 Q UC C V = =∆ Resistance: VI R ∆= 2 2 ohmic heating V Pi V i R R =∆ = =

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Inductance: B,self,sgl coil N L I Φ = back dI L dt ε =− 2 1 2 L UL = I Energy Stored in Fields: 2 2 0 1 22
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Final_2006Fall_Solutions - Physics 8.02 Final Exam Equation...

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