Exam2_2003Fall

# Exam2_2003Fall - Physics 8.02 Some(possibly useful...

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Physics 8.02 Exam Two Mashup Fall 2003 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 0 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 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 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 +

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PHYSICS DEPARTMENT Test No. 2 FAMILY (last) NAME GIVEN (first) NAME Student ID Number Your Section (check one): ___L01 (Hudson) TTh 12-2 ____L02 (Feld) TTh 2-4 Your Group (e.g. 4A): ______________ Instructions: 1. Show all work. All work is to be done in this booklet. 3. This is a closed book test. 4. Calculators and books are not allowed. 5. Do all four problems 6. Print your name on each page of this booklet 7. Crib Sheets are not allowed (Key equations are provided.) Problem Score Grader 1 2 3 4 TOTAL I certify that I have not communicated with anyone about the contents of the 8.02 exam given Thursday evening October 30, 2003 Signed __________________