Physics II Test 2 Sheet - Summary of Equations needed for Exam 2 PDF

Preview

Summary

Summary of Equations needed for Exam 2...

Description

Magnetic Field due to Current with Loop

Force on Conductor w Motional EMF

B=[(µ0I)/(2R)] * N

Fpull=Fmag=ilB=(vlB⁄R)lB=(vl2B2)⁄R

Magnetic Field of a Solenoid

P=E⁄t=(Fd)⁄t=Fv (Power)

B=[(µ0I)/(L)] * N

Pinput=FpullV=(v2l2B2)⁄R (R=resistance)

ΔVloop=ΔV1+ΔV2 +ΔV3+...= 0

Magnetic Force on Moving Charge in a Uniform Magnetic Field

Pdissipated=I2R=(v2l2B2)⁄R=emf2R

Circuit with battery & resistor

F=|q|vBsinϴ=(mv2)/r

Chapter 23- Circuits V= Uelec/q

VB= VR1+VR2

є=V-IR

Kirchov’s Junction Law Kirchov’s Loop Law

r =(mv)/|q|B

Magnetic Flux (Loop) Φ=AeffBcosϴ [Wb]

V=IR

ΔVbat= єmf

v=[2qV/m]^.5

ΔVR= -IR

єmf-IR= 0

Magnetic Force on a Current/ Wire

Aeff=abcosϴ=Acosϴ

Fwire= ILBsin ϴ = |q|vBsinϴ = q(d/t)Bsinϴ =(q/t)dBsin ϴ = IdBsinϴ

Iinduced=єmf⁄R (Induced emf)

Resistors in Series I= єmf/R1+R2

Req=R1+R2

Єmf= |ΔΦ⁄Δt| (Faraday’s Law)

Resistors in Parallel

Torque on a Loop

Єmfcoil=N|ΔΦper coil⁄Δt|=NA|ΔB⁄Δt|

єmf=ΔV1=ΔV2

T=Ttop+Tbottom= .5Ftopsinϴ+.5Fbottomsinϴ =(.5L)ILBsinϴ+(.5L)ILBsinϴ =(IA)Bsinϴ*N (if multiple turns)

Electromagnetic waves

IA= magnetic dipole moment

Ey=E0sin2pi[(x⁄λ)-(t⁄T or ft)]

Charge to Mass ratio of particle moving in a uniform magnetic field

Bz=B0sin2pi[(x⁄λ)-(t⁄T or ft)]

Ibat= I1+I2 =(ΔV1/R1)+(ΔV2/R2)= (єmf/R1) + (єmf/R2) Req (3) = (R1R2R3)/(R1R2+R1R3+R2R3) ^(2)= (R1R2)/(R1+R2)

Capacitor in Parallel

I=P⁄A=.5cє0E02=.5(c⁄µ0)B02 (Intensity)

(q/m)=(2pi/TB)

Qtot=Q1+Q =C1ΔVc+C2ΔVc Ceq=Q/ΔVc=C1+C2 Capacitor in Series ΔV1=Q/C1

C=λf =E0⁄B0 (wave speed) (0=amp)

ΔVc=ΔV1+ΔV2

Ceq=[(1/C1)+(1/C2)+(1/C3)]^-1

Mass Spectrometer U=KqΔV=.5mv

Polarizers

Bar Magnet Magnetic Dipole moment

Etransmitted=Eincidentcosϴ (E of lighttrans)

T=mBsinϴ

m=T/Bsinϴ

Itrans=Einc(cosϴ)2 (Malu’s Law)

Hall Probe Q

ΔVH=(IB)/(tne)

I1=.5I0 (Intensisty polarizer)

Speed Blood Flow

= (C1C2)/(C1+C2)

I=Psource⁄4pir2 (spherical wave) (r=d) 2

ΔVH=vBh

I2=I1cos2ϴ=.5I0cos2ϴ (I analyzer)

Fc=FB-> qE=qvB -> E=vB -> ΔV=Eh=vBh

Ephoton=hf [eV]

Separation Distance r F= (µ0I1I2)/(2pir)

(Q⁄T)=eϭAT4 (rate heat transfer)

I=ΔVc/R (after time “t”)

Electron’s acceleration through a wire

λpeak=2.9*106⁄T [nm] (Wien’s Law)

I=I0e^(-t/RC) or I=I0e^(-t/T)

F=qvB=ma-> a= (qvB)/m = (efcB)/m = (efcµ0I)/2pidm

E dissipated in a resistor Q

Chapter 25-EM Induction & Waves

Wave E through an area A Q E=IAΔt

Motional EMF on Conductor Charge Separation

E Density

FE=qE=FB=qvB (if perp to field)

Power flow per unit Area

E=vB (electric field in conductor)

s=є0cE2[W⁄m2]

ΔV=vlB (potential diff of conductor)

Power Output Antenna Q

єmf=vlB (l=length)

P=I4piR2=(fc⁄2A)4piR2

Ohm’s Law& Induced Current foEr Wire I = E ⁄ R=(vlB) ⁄ R

Force of Light on Polarizer Q

RC Circuits (ΔVc)0=Q0/C

I0=(ΔVc)0/R

ΔVc=(ΔVc)0e^(-t/RC or T) Time Const “T” = RC Capacitor w/ Battery Charging I=I0e^(-t/RC) ΔVc=єmf[1-e^(-t/RC)] Chapter 24-Magnetic Fields/Forces XXX= into

OOO= out of

Magnetic Field due to long straight current/wire:

B=(µ0I)/(2piR)

E=P⁄t=єmf2t⁄R=N2A2t⁄R

u=є0E2

F=pA Iab=I-Itr=I(1-cos2ϴ)

Chapter 26-AC Electricity Emf of AC Voltage Source Є=є0cos(2pifT)=є0cos(2pit⁄T) (є⁄R)=(є0⁄R)cos…i=i0cos… Inst. Resistor Voltage

vR=iRR

RLC Circuit resonance freq Xc=XL f0=[1⁄2pi√(LC)] Max Current when Circuit at Resonance f z=R I=(V⁄Z)=(V⁄R)

ϴmin=(1.22λ⁄D)=d⁄L=sinϴm=ϴm L=(dD)⁄(1.22λ) Mars min Feature Size Q d=(1.22λL)⁄D

Z=√[R2+(XL-XC)] XC=XLf0=(1⁄2pi√LC)

Chapter 18-Ray Optics

RLC Circuit with Angular Frequency “w”Q

ϴi=ϴr (Law of Reflection)

Xc=XL(1⁄wc)=wLw2=(1⁄LC)L=(1⁄ w2C)

S’=S (plane mirror)

Phase Angle of RLC Circuit Q

n1sinϴ1=n2sinϴ2 (Snell’s Law, n= refr)

Z=√[R2+(XL-XC)2]

ϴc=sin-1(n2⁄n1) (critical angle if n increase)

tanΦ=(XL-XC)⁄R

l=stanϴ1=s’tanϴ2s’=(tanϴ1⁄tanϴ2)s

Current with 1 resistor in circuit

*^voltage step down vv

(sinϴ1⁄sinϴ2)=(n2⁄n1)=abt (tanϴ1⁄tanϴ2)

iR=(vR⁄R)=(VRcos(2pift)⁄R)=IRcos…

# Turns Secondary Coil Q

m=-(s’⁄s) (magnification or orientatiom)

(Vp⁄Vs)=(Np⁄Ns)=(IS⁄Ip)

|m|=(h’⁄h) (ratio image height to obj height)

Chapter 17-Wave Optics

(h’⁄h)=(s’-f)⁄f(1⁄s)=(s’-f)(⁄s’f)=(1⁄f)-(1⁄s’)

f=(v⁄λ)=(c⁄λ) n=(c⁄v) (index refract)

(h’⁄h)=(s’⁄s)

Kirchov’s Loop Law&Resistor Circuit ΔVtotal= ΔVsource+ΔVR = є-vR = 0 Resistor Voltage @ Sinusodial freq vR=(VR⁄R)=(VRcos(2pift)⁄R)=IRcos(2pi ft)

IR=VR⁄R (peak current) AC Power in Resistors P=iR2R=[IRcos(2pift)]2R=IR2R[cos(2pift)]2

PR=.5IR2R (average power) Irms=(IR⁄√2)

Vrms=(VR⁄√2) (root mean sq)

Average Power lost in Resistor PR=Irms2R=(Vrms2⁄R)=IrmsVrms Transformers V1or2=є1or2=N1or2(ΔΦ⁄Δt) [Faraday’s Law] (v1⁄v2)=(N1⁄N2)=(i1⁄i2) [ratio inst voltage] V2=(N2⁄N1)V1 or V2(rms)=(N2⁄N1)V1(rms) I2=(N1⁄N2)I1

or

I2(rms)=(N1⁄N2)I1(rms)

vc=Vccos(2pift)

λmat=(v⁄fmat)=(c⁄nfvac)=(λvac⁄n)

(1⁄s)+(1⁄s )=(1⁄f)

asinϴ=pλ (comp destruct intf)

Laser Aimed at Mirror Question

ϴp=p(λ⁄a) (angle in rad of dark fringe w slit)

ϴr=ϴi=tan-1(l⁄h)

yp=(pλL⁄a) (dark fringe location)

ϴi+Φ=90ϴi=90-Φ

Δr=mλ (construct interference&bright)

Index Refr w Crititcal Angle__

y=Ltanϴ (bright point on screen)

n1sinϴc=n2sin(90)

Δr=dsinϴm=mλ (where both fringe occur)

q=Cvcvc=(q⁄C)

*”from mirror=-s’*

Δy=ym+1-ym=((m+1)λL⁄d)-(mλL⁄d)=(λL⁄d) (spacing between bright fringe)

ic=C(Δvc⁄Δt) (peak value)

Interference of reflected Light

Capacitive Reactance

2t=m(λ⁄n) (construct int,t=dist)

Ic=(Vc⁄XC)Vc=(peak current or volt)

2t=(m+.5)(λ⁄n) (destruct)

Inductor(L)& Inductor Circuits

Circular Aperture Diffraction

vL=L(ΔiL⁄Δt) (inst inductor voltage)

w=2yp=2Ltanϴ1=(2.444pλL⁄D) (width central max fr diam D) ϴ1=(1.22λ⁄D) (1st min instensity)

VL=L(2pifIL)=(2pifL)IL (peak val ind vol)

Soap Bubble Q

IL=(VL⁄XL)VL=ILXL (peak I&V inductor)

*d is slit separation*

XL=2pifL=wL (peak inductive reactance[Ω]) LC Circuit f=(1⁄2pi)√(k⁄m)

h'=(s’⁄s)h

ϴm=(mλL⁄d) (small angle, d-slit spacing)

y’m=(m+.5)(λL⁄d) (dark fringe location)

vL=VLcos(2pift) (in parallel, L [H])

Image height Q

Radius Curvature Spherical Mirror Rc=2f

ic=(Δq⁄Δt) (cap current)

XC=(1⁄2pift)

(Thin Lens Equation)

***Δr=(1+.5)λ for dark

ym=(mλL⁄d) (pos of mth fringe, L screen dist)

Capacitor Circuits

(image real or virtual)

’

d=(λ⁄4n)m

Vehicle on Desert Road Headlights...