Exam2_2005Spring_Solutions

Exam2_2005Spring_Solutions - Physics 8.02 Exam Two Mashup...

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Physics 8.02 Exam Two Mashup Solutions Spring 2005 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 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 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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MIT PHYSICS DEPARTMENT ` page 2 Problem 1: Five Short Questions. Circle your choice for the correct answer. Question A (5 points out of 25 points): A charge +2q moves vertically upward with speed V . A second charge -q moves horizontally to the right with the same speed V . Finally, a third charge +q moves horizontally to the right with the same speed V . The point P is located a perpendicular distance a away from each charge, as shown in the figure. The magnetic field at point P is (a) Into the page with magnitude 2 2 4 o qV a µ π (b) Into the page with magnitude 2 4 4 o qV a (c) Out of the page with magnitude 2 2 4 o qV a (d) Out of the page with magnitude 2 4 4 o qV a Question B (5 points out of 25 points): A positive charge enters a region of perpendicular electric and magnetic fields as shown in the figure, traveling with speed V o directed horizontally to the right. Initially the charge m through the region shown w no deflection and emerges through the hole in screen S oves ith 2 . If we now want the charge to hit below the hole in the screen S 2 , we should (a) Decrease its speed below V o or increase the magnitude of E.
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Exam2_2005Spring_Solutions - Physics 8.02 Exam Two Mashup...

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