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Exam3_EquationSheet

Exam3_EquationSheet - Physics 8.02 Exam Three Please Remove...

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Physics 8.02 Exam Three Fall 2007 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: 2 1 ˆ 4 o dq d r πε = E r G free, inside closedsurface o Q d κ ε = ∫∫ E A G G w points from inside to outside d A G total d d dt dt ε Φ = − = − ∫∫ E ds B dA G G G G v moving from to b a b b a a V V V d Δ = = − E s G 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 where points source observer r from to 0 closed surface d = ∫∫ B A G G w through 0 contour E o d d I dt μ ε Φ = + B s G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d = J A G G d s is right-handed with respect to d A 2 2 0 1 2 2 E B o B u E u ε μ = = ( ) ext q = + × F E v B G G G G ext d I d = × F s B G G G 2 cent. F mv r = IA = μ n G ± = × τ μ B G G G z z z dB F dz μ = V IR Δ = L R A ρ = 2 2 ohmic heating V P I V I R R Δ = Δ = = Q C V = Δ parallelplate o A C d ε = 2 2 1 2 2 Q U C V C = Δ = 1 C RC X C τ ω = = B,self,total back dI L L I dt ε Φ = = − 2 1 2 L U LI = / L L R X L τ ω = = Series RLC: ( ) 2 2 2 2 tan L C Z R X R X X X R ϕ = + = + = 2 2 2 f T k ω = π = π = π λ ( ) 1 2 0 0 c T f k = λ = λ = ω = μ ε 0 light 0 ˆ ˆ ˆ E v B = × = E B p absorb reflect 0 1 2 ; S S P P c c = × = = μ S E
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