Exam2_2006Spring_Solutions

# Exam2_2006Spring_Solutions - Physics 8.02 Exam Two...

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Physics 8.02 Exam Two Solutions Spring 2006 Please Remove this Tear Sheet from Your Exam Some (possibly useful) Relations: inside,free closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G moving from to b ab b a a VV V ∆= = Es G d G 0 d −⋅= G G v many point charges 1 4 N i i oi q V πε = = rr GG V Q C = C Q V = parallelplate o A C d = U = 1 2 C V 2 = Q 2 2C series 1 2 11 1 CC C =+ parallel 1 2 C where is the resistivity ρρ = EJ 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 Pi V i R R =∆ = = 2 ˆ 4 o q c r µ π × = << vr Bv G G G 2 ˆ r 4 o I d d × = B sr G G ˆ points source observer rf r o mt o through contour o dI Bs G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d = JA G G d s right-handed with respect to d A sgl loop d d N dt dt Φ = Ed s BdA G G v ext q Fv B G G G ext d Fs B G 2 cent. Fm v = r = perpendicular to loop, right-handed with respect to IA I μ nn G ± ± = × τ μB G G G z zz dB F dz = Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆˆ ˆ × = ijk ˆ × = j ki ˆ × = ki j Some potentially useful numbers 2 97 2 0 1N m 91 0 4 1 0 4C eo k µπ == × = × 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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MIT PHYSICS DEPARTMENT p. 2 of 10 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (5 points out of 20 points): The picture below shows an iron filings representation of the magnetic field surrounding two parallel, current carrying wires. Which of the following statements is true? The magnetic force on the left-hand wire is… 1) to the right and larger in magnitude than the magnetic force on the right hand wire 2) to the right and equal in magnitude to the magnetic force on the right hand wire 3) to the right and smaller in magnitude than the magnetic force on the right hand wire 4) to the left and larger in magnitude than the magnetic force on the right hand wire 5) to the left and equal in magnitude to the magnetic force on the right hand wire 6) to the left and smaller in magnitude than the magnetic force on the right hand wire 7) zero 8) I don’t know (this answer is worth 1 point) Wires are clearly repulsive, and forces must be equal (and opposite) Question B (5 points out of 20 points): You are given two long straight pieces of wire and a semicircle of wire and asked to construct a shape that, when a current is passed through it, creates a large B field at the center of the semi-circle (that is, the center of the circle from which the semi-circle is cut). You construct: Rank the strength of the B field generated by these three configurations (assuming the current is the same in each): 1) 2) C > B > A 3) A = C > B 4) B > A = C 5) A > B = C 6) A = B = C 7) I don’t know (this answer is worth 1 point) In A the legs and loop make a field in the same direction. In B the legs don’t contribute.
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## This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Spring '07 term at MIT.

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Exam2_2006Spring_Solutions - Physics 8.02 Exam Two...

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