Exam2_2007Spring

Exam2_2007Spring - Physics 8.02 Equation Sheet Exam Two...

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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
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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
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8.02 Exam Two Spring 2007 FAMILY (last) NAME GIVEN (first) NAME
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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.

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Exam2_2007Spring - Physics 8.02 Equation Sheet Exam Two...

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