Exam2_2007Spring

Exam2_2007Spring - Physics 8.02 Equation Sheet Exam Two...

This preview shows pages 1–4. Sign up to view the full content.

Physics 8.02 Equation Sheet Exam Two Please Remove this Tear Sheet from Your Exam Force Laws: () ext ext q =+ × FEv B GG G G Source Equations: 2 1 ˆ 4 o dq d r πε = Er G 2 ˆ 4 o I d d r µ π × = sr B G G ˆ r r r= G points from source to field point Current Density and Current: open surface I d =⋅ ∫∫ Ja G G Gauss’s Law: inside closedsurface o Q d ε ⋅= EA G G w Ampere’s Law: closed path open surface o dd Bs v Gauss’s Law for Magnetism: 0 closed surface d BA G G w Faraday’s Law: magnetic d dt =− Φ For Current Loops: total single turn magnetic magnetic N Φ= Φ Electric Potential Difference: b ba a VVV d ∆= − ≡ − ⋅ Es G G Capacitance: V Q C = 2 2 11 22 Q UC C V = =∆ Capacitors in Parallel: 12 eq CCC = + +⋅⋅⋅ Capacitors in Series: 111 eq = + Ohm’s Law: VI R = where is the conductivity cc σσ = JE G G where is the resistivity rr ρρ = EJ G G Resistors in Parallel: eq RRR =++ Resistors in Series: eq = + Joule Heating: 2 2 Joule V PI V I R R =∆ = = Magnetic Dipoles : = I A μn G ± Torque: = × τ μB G G G Force: z zz dB F dz = Cross-products of unit vectors : ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆˆ ˆ × = ijk ˆ × = j ki ˆ ×= ki j Kinematics: 2 / cent vr = a G 2 2 f T ωπ == 1

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

View Full Document
Circumferences, Areas, Volumes: 1) The area of a circle of radius r is Its circumference is π r 2 2 r 2) The surface area of a sphere of radius r is . Its volume is 4 r 2 3 (4 / 3) r 3) The area of the sides of a cylinder of radius r and length is l 2 rl . Its volume is 2 rl Integrals that may be useful dr a b = b a ln( / ) b a dr ba r = 1 r 2 dr a b = 1 a 1 b Some potentially useful numbers 92 0 1 91 0Nm C 4 e k πε - 2 = 7- 0 10 T m A 4 1 µ = ⋅⋅ 2
8.02 Exam Two Spring 2007 FAMILY (last) NAME GIVEN (first) NAME

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

This test prep was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

Page1 / 19

Exam2_2007Spring - Physics 8.02 Equation Sheet Exam Two...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online