Exam2_2004Fall_Solutions

Exam2_2004Fall_Solutions - Physics 8.02 Exam Two Mashup...

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Physics 8.02 Exam Two Mashup Solutions Fall 2004 Some (possibly useful) Relations: inside 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 G d 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 CC =+ 1 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 opdfden 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 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 μn n 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 1 N m T m 91 0 4 1 0 4C eo k µπ == × = × 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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8.02 2 nd Exam Name_____________________ Problem 1 (25 Points) Circle your choice for the correct answer to the five questions below. A: A particle with known charge q and known mass m is performing circular motion in a uniform magnetic field of known magnitude B (as usual, the orbit is perpendicular to the magnetic field). With q, m , and B known, examine the following statements: (a) The radius R of the orbit can be determined uniquely. (b) The speed v of the particle can be determined uniquely. (c) The angular velocity ω of the particle can be determined uniquely. Circle the one correct statement below 1. Only (a) is correct. 2. Only (b) is correct. 3. Only (c) is correct CORRECT 4. Only (a) and (b) are correct. 5. Only (a) and (c) are correct. 6. Only (b) and (c) are correct. 7. All are correct. 8. None is correct B: Consider an infinitely long cylindrical solenoid of radius R with n turns per unit length and a current I . The magnetic field due to this solenoid satisfies: 1. for r < R and 0 B = 0 B nI µ = for r > R .
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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_2004Fall_Solutions - Physics 8.02 Exam Two Mashup...

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