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### Exam3_EquationSheet

Course: 8 8.02, Fall 2007
School: MIT
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Word Count: 322

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8.02 Exam Physics Three Please Remove this Tear Sheet from Your Exam Fall 2007 Some (possibly useful) Relations: 1 dq ^ dE = r 4 o r 2 Qfree, inside E dA = closedsurface o dA points from inside to outside A Q Cparallelplate = o d V 2 1 U = C V 2 = Q 2C 2 = RC X C = 1 C C= L= B,self,total I E ds = - dt B dA d =- b d total dt back = - L dI dt Vmoving from a to b = Vb - Va = - E d s a U L...

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8.02 Exam Physics Three Please Remove this Tear Sheet from Your Exam Fall 2007 Some (possibly useful) Relations: 1 dq ^ dE = r 4 o r 2 Qfree, inside E dA = closedsurface o dA points from inside to outside A Q Cparallelplate = o d V 2 1 U = C V 2 = Q 2C 2 = RC X C = 1 C C= L= B,self,total I E ds = - dt B dA d =- b d total dt back = - L dI dt Vmoving from a to b = Vb - Va = - E d s a U L = 1 LI 2 2 ^ q vr B= o 2 4 r ^ I ds r v << c dB = o 2 4 r = L/R X L = L Z = R2 + X 2 = R2 + ( X L - X C ) tan = X R k = 2 - 12 2 ^ where r points from source to observer Series RLC: closed surface B dA = 0 = 2f = 2 T dE B d s =o I through + 0 dt contour where Ithrough is the current flowing through any open surface bounded by the contour: I through = J dA c = = T f = k = ( 0 0 ) ^ ^ ^ E0 = vlight B0 EB = p S= 1 EB 0 Pabsorb = S 2S ; Preflect = c c open surface ds is right-handed with respect to dA 1 B2 uE = 0 E 2 uB = 2 2o F = q E + v B ext If the function D(t ) satisfies the equation d D(t ) D(t ) = - , then D(t ) = Do e -t / dt Cross-products of unit vectors: ^^ = ^^ = k k = 0 i i j j ^ ^ ^^ = k ^k = ^ k ^ = ^ i j ^ j ^ i ^ i j ( ) dF = I d s B ext Fcent. = mv 2 r = IA n = B V = IR Fz = z R= 2 dBz dz L A Pohmic heating V 2 = I V = I R = R Some potentially useful numbers 1 N m2 Tm ke = = 9 109 o = 4 10-7 2 4 0 C A 6 Breakdown of air E ~ 3 x 10 V/m Earth's B Field B ~ 5 x 10-5 T = 0.5 Gauss Speed of light c = 3 x 108 m/s Light (blue to red) = 400 nm to 700 nm Electron charge e = 1.6 x 10-19 C Avogadro's number NA = 6.02 x 1023 mol-1
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MIT - 8 - 8.02
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