Exam1_2004Spr_Solutions

Exam1_2004Spr_Solutions - Physics 8.02 Exam One Solutions...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 8.02 Exam One Solutions Spring 2004 PLEASE DETACH THIS SHEET AND USE AT YOUR CONVENIENCE Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 2 3 ˆ 4 4 o o q q r r πε πε = = E r G r G ˆ points source q observer r r r = from to G 2 0 1 ˆ 4 V dq r πε = E r G inside o closed surface Q κ ε = ∫∫ E dA 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 πε = many point charges 1 4 N i i o i q V πε = = r r G K = pairs all j i o j i q q U r r G G πε 4 2 1 2 o v U E ε = ∫∫∫ x ol dV E x = - V x , E y = - V y , E z = - V z Q C V = U = 1 2 C V 2 = Q 2 2C o parallel plate A C d κ ε = 1 parallel C C 2 C = + 1 2 1 2 series C C C C 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 π r 2 Its volume is 3 4 3 r π 3) The area of the sides of a cylinder of radius r and height h is 2 π r h Its volume is π 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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon