Exam2_2004Spring

Exam2_2004Spring - Physics 8.02 Exam Two Mashup Fall 2004...

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Unformatted text preview: Physics 8.02 Exam Two Mashup Fall 2004 Some (possibly useful) Relations: inside 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 ∆ = − = − ∫ E s G G d ⋅ d − ⋅ = ∫ E s G G v many point charges 1 4 N i i o i q V πε = = − ∑ r r G G V Q C ∆ = C Q V = ∆ parallelplate o A C d ε = U = 1 2 C ∆ V 2 = Q 2 2C series 1 2 1 1 C C = + 1 C parallel 1 2 C C = + C where is the resistivity ρ ρ = E J G G ∆ V = i R L R A ρ = 1 R parallel = 1 R 1 + 1 R 2 R series = R 1 + R 2 2 2 ohmic heating V P i V i R R ∆ = ∆ = = 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 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 right-handed with respect to d A sgl loop d d N dt dt ε Φ ⋅ = − ⋅ = − ∫ ∫ E ds B dA v 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 × = × = × = i i j j k k ˆ ˆ ˆ × = i j k ˆ ˆ ˆ × = j k i ˆ ˆ ˆ × = k i j Useful integrals: 1/ 2 1/ 2 2 ( ) ( ) d c f c f f θ θ θ = + + ∫ 1 ln( ) ( ) d c f c f f θ θ θ = + + ∫ 2 1 1 ( ) ( ) d c f f c f θ θ θ = − + + ∫ Useful Small Argument Approximations (1 ) 1 for <<1 n n ε ε ε + ≅ + ln(1 ) for <<1 ε ε ε + ≅ 8.02 2 nd Exam Name_____________________ Problem 1 (25 Points) Circle your choice for the correct answer to the six questions below. A: Eight parallel wires cut the page perpendicularly at the points shown. All the wires carry the same magnitude of current I , but some carry current into the page and some carry current out of the page. For those with k = 1 to 4, the current flows up out of the...
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This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Exam2_2004Spring - Physics 8.02 Exam Two Mashup Fall 2004...

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