Exam1_2005Spr_Solutions

# Exam1_2005Spr_Solutions - Physics 8.02 F= Exam One...

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Physics 8.02 Exam One Solutions Spring 2005 F = 1 4 πε o q 1 q 2 r 2 23 ˆ 44 oo qq rr == Er G r G ˆ points source q observer r r r= from to G 2 0 1 ˆ 4 V dq r = G inside o closed surface Q κ ε ⋅= ∫∫ EdA G G w outside to inside from points A d G = = b a a b b to a from moving V V V s d E G G 0 = path closed s d E G G point charge 4 o q V r = many point charges 1 4 N i i oi q V = = G K = pairs all j i o j i q q U r r G G 4 2 1 2 ov UE ⎡⎤ = ⎢⎥ ⎣⎦ ∫∫∫ x o l d V E x = - V x , E y = - V y , E z = - V z r V E r =− for spherical symmetry Q C V = U = 1 2 C V 2 = Q 2 2C 1 parallel CC 2 C = + 12 series C = + Circumferences, Areas, Volumes: 1) The area of a circle of radius r is π r 2 Its circumference is 2 π r 2) The surface area of a sphere of radius r is 4 r 2 Its volume is 3 4 3 r 3) The area of the sides of a cylinder of radius r and height h is 2 r h Its volume is r 2 h Definition of trig functions sin is opposite/hypotenuse; cos is adjacent/hypotenuse; tangent is opposite over adjacent; Properties of 30, 45, and 60 degrees ( π /6, π /4, and π /3 radians) : sin( π /6) = cos( π /3) = 1/2, sin( π /3) = cos( π /6) = 2 / 3; sin( π /4) = cos( π /4) = 2 / 1 ; Integrals that may be useful a b dr b a = ) / ln( 1 a b dr r b a = = b a dr r b a 1 1 1 2

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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): The field line to the right is a field line of the vector field a) ˆˆ ( , ) sin( ) x yx =+ Fi G j CORRECT b) (, ) c o s () x =− G j c) s i n x G j d) c o s x G j 2 egative e) None of these I1 I2 O1 O2 Question B (5 points out of 25 points): Two hollow conducting shells are concentric. They carry no net charge. We place a negative point charge at the center of the shells. Let V be the potential at O1 and V be the potential at O2. Then 1 O 2 O a) and the surface charge at O2 is n 1 OO VV > b) ace charge at O2 is negative 12 < and the surf CORRECT c) e surface charge at O2 is negative = and th d) and the surface charge at O2 is positive > e) and the surface charge at O2 is positive < f) and the surface charge at O2 is positive =
MIT PHYSICS DEPARTMENT ` page 6 Question C (5 points out of 25 points): We have two electric dipoles. Each dipole consists of two equal and opposite point charges at the ends of an insulating rod of length d . The dipoles sit along the x- axis a distance r apart, oriented as shown below. The dipole ON THE LEFT : 1. will feel a force upwards and a torque trying to make it rotate clockwise 2. will feel a force upwards and a torque trying to make it rotate counterclockwise CORRECT 3. will feel a force upwards and no torque 4. will feel a force downwards and a torque trying to make it rotate clockwise.

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## This homework help 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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Exam1_2005Spr_Solutions - Physics 8.02 F= Exam One...

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