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Phys222_Formulas_F2007

Phys222_Formulas_F2007 - Physics 222 constants o = 4 10-7...

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Physics 222 Formula Sheet constants: µ o = 4 π × 10 7 T·m/A e = 1.602 × 10 19 C m e = 9.11 × 10 31 kg ε o = 8.854 × 10 12 C 2 /N·m 2 m p = 1.67 × 10 27 kg c = 3.00 × 10 8 m/s h = 6.626 × 10 34 J·s = 4.136 × 10 15 eV·s = h 2 π = 1.055 × 10 34 J·s = 6.583 × 10 16 eV·s µ B = e 2m e = 9.274 × 10 24 J/T = 5.789 × 10 5 eV/T N A = 6.022 × 10 23 (mol) 1 k = 1.381 × 10 23 J K = 8.617 × 10 5 eV K R = N A k = 8.314 J mol·K = 0.08208 L·atm mol·K units, conversions: 1 N = 1 kg·m/s 2 1 J = 1 N·m = 1 kg·m 2 /s 2 1 eV = 1.602 × 10 19 J 1 = 1 V/A 1 T = 1 N/(A·m) 1 H = 1 Wb/A = 1 V·s/A = 1 ·s = 1 J/A 2 1 Wb = 1 T·m 2 1 Pa = 1 N/m 2 1 L·atm = 101.3 J prefixes: c = 10 2 m = 10 3 µ = 10 6 n = 10 9 p = 10 12 f = 10 15 k = 10 3 M = 10 6 G = 10 9 T = 10 12 geometry: circle: C = 2 π R A = π R 2 sphere: A = 4 π R 2 V = 4 3 π R 3 cylinder: V = π R 2 L A = 2( π R 2 ) + 2 π RL vectors: A ·B = AB cos φ A ·B = A x B x + A y B y + A z B z A ˆ = A /A A × B = (A y B z A z B y ) i ˆ + (A z B x A x B z ) j ˆ + (A x B y A y B x ) k ˆ | A × B | = AB sin φ calculus: d sin[u(t)] dt = du(t) dt cos[u(t)] d cos[u(t)] dt = du(t) dt sin[u(t)] d a t n dt = a n t n 1 mechanics: F = m a a c = v 2 /r τ = r × F = d L /dt = I cm α τ = r F sin φ = I cm α dW = F · d r W = KE electricity: F E = q E V C = q/C U E = q 2 /(2C) = CV C 2 /2 u E = ε o E 2 /2 J = n q v dr J = σ E i = J A i = V/R Note: In this formula sheet the symbols v or V are used for EMF (electromotive force or voltage) instead of script E. Note that v is also used to symbolize speed. Ch. 27 F = q v × B F = |q| v B sin φ Φ B = B · d A Φ B = B · A = B A cos φ O B · d A = 0 |q|vB = mv 2 /R R = mv |q|B f = ω 2 π = 1 T = |q|B 2 π m F = q E + q v × B v = E/B F = I × B F = I B sin φ d F = I d × B U = −µ · B = −µ B cos φ µ = N I A µ = N I A τ = µ × B τ = µ B sin φ = N I A B sin φ Ch. 28 d B = µ o 4 π I d × r ˆ r 2 dB = µ o 4 π I d sin φ r 2 wire: B = µ o I 2 π r B = µ o Ir 2 π R 2 center of circular arc (rad): B = µ o I φ 4 π R coil: B = µ o NI 2R 2 parallel wires: F = µ o I 1 I 2 2 π d O B · d = µ o I encl toroid: B = µ o N I 2 π r solenoid: B = µ o n I = µ o N I
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Ch. 29 V = N d Φ B dt Φ B = B · d A = B dA cos φ Φ B = B · A = B A cos φ V = B v I = V R P = I 2 R = IV = F ext ·v v = NAB ω sin( ω t) O E d = d Φ B dt solenoid: outside: E = 1 2 π r d Φ B dt = A 2 π r dB dt inside: E = r 2 dB dt O B · d = µ o (i C + i D ) encl i D = ε 0 d Φ E /dt Φ E = E · d A Φ E = E · A = E A cos φ Ch. 30 v 2 = M d i 1 dt v 1 = M d i 2 dt M = N 2 Φ B2 i 1 = N 1 Φ B1 i 2 v L = L d i d t L = N Φ B i solenoid or toroid: L = µ o N 2 A = µ o n 2 A = µ o n 2 ·volume U B = 1 2 L i 2 u B = B 2 2 µ o RL circuit: i = V R (1 e t/ τ ) i = i 0 e t/ τ τ = L R LC circuit: q = Q cos( ω t) i = I sin( ω t) I = ω Q ω = 1  LC ω = 2 π f T = 1 f = 2 π  LC U = U E + U B = q 2 2C + L i 2 2 = Q 2 2C = L I 2 2
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