Crib2Edited - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

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Constants k=1/(4 πε 0 )=8.99x10 9 (N*m 2) /C 2 ε 0 =8.85x10 -12 C 2 /(N*m 2 ) e - = -1.6 x 10 -19 C μ 0 =4πe-7 T*m/h μ 0 =1.26x10 -6 c=speed of light=3.0 x 10 8 m/sec speed of sound (air) = 343 m/sec Φ B = Magnetic Flux (Weber, W) Φ E = Electric Flux ((N*m 2) /C) B = Magnetic Field (Tesla, T) L = Inductance (Henry, H [V*s/A]) Є = emf (volts) Area Circle = π r 2 Circumference Circle = 2 π r Surface Area Sphere = 4 π r 2 Inductance (L) Unit for L = H (Henry) Є = -( d Φ B / d t) = §E* d s Faraday’s Law L=NΦ B /i N= # windings A = cross sectional area n = # turns per unit length l = unit length Φ B =A(μ 0 in) [solenoid] L= μ 0 n 2 lA [solenoid] N=nl Є L = -N( d Φ B / d t)= -L( d i/ d t) self-induction U B = ½ Li 2 energy stored in inductor u B =B 2 /(2μ 0 ) u E = ½ ε 0 E 2 energy density Magnetic Fields Φ B = §B* d A = 0 Φ B =BA Gauss’ Law §B* d s = μ 0 ε 0 ( d Φ E / d t) Maxwell’s Law of Induction §B* d s = μ 0 ε 0 ( d Φ E / d t) + μ 0 i enc Ampere-Maxwell Law i d 0 ( d Φ E / d t) Displacement Current §B* d s = μ 0 i d + μ 0 i enc i d – wherever changing E field i = i d q=CV C= ε 0 (A/d) V=Ed For Capacitor q=ε 0 (A/d)Ed=ε 0 (A*E)= ε 0 E i=(d q/ d t)=ε 0 ( d Φ E / d t)= i d Simple Harmonic Motion mass - kg x=x m cos(ωt+ø) x – disp., x m –amp (m) (ωt+ø) – phase (rad) ø – phase constant (rad) ω – angular frequency (rad/s) ω = 2π/T = 2πf ω = √(k/m) T = (2π)/ω = 2π*√(m/k) f = 1/T = ω/(2π) = (1/(2π))*√(k/m) v = d x/ d t= -ωx m sin(ωt+ø) ωx m = velocity amp. a = -ω 2 x m cos (ωt+ø) = (-kx)/m ω 2 x m = acceleration amp. Mass on a Spring v max = ω x max F=-kx F=ma m( d 2 x/ d t 2 )=-kx x = disp. from equilibrium K= ½ mv 2 = ½ k x m 2 sin 2 (ωt+ø) Kinetic (max at equilibrium) k = mω 2 U= ½ kx 2 = ½ k x m 2 cos 2 (ωt+ø) Potential (max at end points) E = K+U = ½ kx m 2 E = K max = U max f=[1/(2π)]* √(k/m) LC Energy Transfers L – Henry; C –Farad U E = q 2 /(2C) = (Q 2 /(2C))*cos 2 (ωt+ø) U = U B + U E -> is Constant U B = ½Li 2 = (½LI 2 )*sin 2 (ωt+ø) U B max = U E max (unit: J) L( d 2 q/ d t 2 ) + (1/C)q = 0 Li 2 = Q 2 /C q=Qcos(ωt+ø) ω=1/√(LC) Q = charge amp. I = current amp. i=-I sin(ωt+ø) I=ωQ d i/ d t = -ωI cos (ωt + ø) = -ω 2 q L( d 2 q/ d t 2 ) + 1/(R( d q/ d t) + (1/C)q = 0 RLC Circuit q=Qe^((-Rt)/(2L)) cos (ω’t + ø) ω’ = √(ω 2 – (R/(2L)) 2 ) T = 2π√(LC) ΔV circuit = -L( d i/ d t) – (q/C) = 0 Loop Rule i= ( d q/ d t) ( d 2 q/ d t 2 ) = -q/(LC) = -(1/(LC))*q V C =-V L =q/C=(Q/C)*cos(ωt+ø) I 2 =Q 2 /LC=ω 2 Q 2 I=ωQ E field =F/ q 0 =k(q)/r 2 (units: N/C) (for a point charge) § E * dA =q/ε 0 EA=q/ ε 0 Maxwell’s Equations: §E* d A=q/ ε 0 §E* d s= -
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This note was uploaded on 04/07/2008 for the course ENG 1000 taught by Professor Broomer during the Spring '08 term at Rensselaer Polytechnic Institute.

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Crib2Edited - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

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