# Crib2Edited-2 - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

This preview shows pages 1–2. Sign up to view the full content.

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) 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 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) Kenetic (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 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) f = 1/2π * 1/√(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

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 note was uploaded on 04/17/2008 for the course PHYSICS 1200 taught by Professor Peterpersans during the Spring '08 term at Rensselaer Polytechnic Institute.

### Page1 / 3

Crib2Edited-2 - Constants k=1/(4 0)=8.99x109 (N*m2)/C2 -12...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online