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Exam2_2007Fall_Solutions

# Exam2_2007Fall_Solutions - Physics 8.02 Exam Two Solutions...

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Physics 8.02 Exam Two Solutions Fall 2007 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: inside, free closedsurface o Q d κ ε = ∫∫ E A G G w points from inside to outside d A G moving from to b a b b a a V V V Δ = = − E s G d G many point charges 1 4 N i i o i q V πε = = r r G G V Q C Δ = C Q V = Δ U = 1 2 C Δ V 2 = Q 2 2C series 1 2 1 1 1 C C C = + ; parallel 1 2 C C = + C Δ V = i R L R A ρ = series 1 2 parallel 1 2 1 1 1 ; R R R R R R = + = + 2 2 ohmic heating V P i V i R R Δ = Δ = = 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 through contour o d I μ = B s G G v where through open surface I d = ∫∫ J A G G d s right-handed with respect to d A sgl loop d d N dt dt ε Φ = − = − ∫∫ E ds B dA G G v 2 2 0 1 2 2 E B o B u E u ε μ = = B,self,total back dI L L I dt ε Φ = = − 2 1 2 L U LI = ext q = × F v B G G G ext d I d = × F s B G G G 2 cent. F mv = r = perpendicular to loop, right-handed with respect to I A I μ n n G ± ± = × τ μ B G G G z z z dB F dz μ = Cross-products of unit vectors: ˆ ˆ ˆ ˆ ˆ ˆ 0 × = × = × = i i j j k k ˆ ˆ ˆ × = i j k ˆ ˆ ˆ × = j k i ˆ ˆ ˆ × = k i j Some potentially useful numbers 2 9 7 2 0 1 N m 9 10 4 10 4 C e o k μ π πε = = × = × T m A Breakdown of air E ~ 3 x 10 6 V/m Earth’s B Field B ~ 5 x 10 -5 T = 0.5 Gauss Speed of light c = 3 x 10 8 m/s Electron charge e = 1.6 x 10 -19 C Avogadro’s number N A = 6.02 x 10 23 mol -1

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