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Virginia Tech - Study Guide - Final

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FINAL EXAM CHEAT SHEET

Ch 25 / 26 - Geometrical Optics

Ch 18 - Electric Forces & Fields

charge of electron c = 9.110 kg mass of electron = 1.00x100

special case: EA - 9/E Coulomb's law

Definitions - E A F.I = k (19.4 )

E = E + E, ET = | E 005(0) k: Coulomb's constant k = 9.99x10 Nmic If you want to learn more check out fau minors

e: blw & marmolto sic, no contribution to thru A Electric Fields

Definition: 0.- E Acose) F = 9E

How much of E, is intercepted by S? E = clectric field (NC)

If you want to learn more check out culearn carleton

If q is outside, 0 = 0 F is inside: 10 F = electrostatic force

Gauss's Law •.- 4.E. Euco a point charge

E. = constant = 8.8.5x03 C/Nm* E = kair) 0> . E: radially outward 040--E: radially inward

MOS

T

=

1

1

MIRRORS

LENSES concavo conv convex diverge

Convex conly concavo diverge Lww of Reaction Don't forget about the age old question of math 136

Conv Lange Tracing

mirror lense aq is the same = real, inverted image e = angle of incedence Don't forget about the age old question of csu canvas

Div Lense Tracing e = angle of reflection

d<0,01 <d,h ch c 1 virtual, uprigh: Normal to sto (all angles

Simple Ortical Deviser Eve General measured from normal)

Eye: Geometries Opis

Image must be real =lens must be converging Mirror / Larse Equation:

Mirror / lense e applics, d = variable & d = foced valid for all cases We also discuss several other topics like uncw surplus

Is there a max d.? Sign convention:

d .& all rays become horizontal & fed d. novor nag for us

Camera: d> 0 if image is real m> 0 7 image is upright (virtual) Must have a real image. Cory lens d<0 if image is virtual m< if image is inverted (real) Lens must be able to move h> 0 if image is upright If you want to learn more check out integrated principles of biology

Constraint: fis fixed h <0 if image is inverted

d.is variable, d must be variable f> O for converging mirrors / lenses fe for diverging mirrors / lanses

For Lenses Magnification

Image forms on same side as observer reall m= h/h, m. m.m.m....m.

Converging lense **If you put object on focal point no image (d ** Image forms on opp side as observer - virtua Snel's Law Index of Refraction

Diverging lense n,sinfe) = n sin( n=alv . 21 air - vacuum, som -1

For Mirrors e. - arcsini nin)

Image forms on same side as observer real image angle of refraction = 90, forn, >n

Concave mirror He increases -e, also increases

Image forms on opp side as observer - virtual image Max value of e, - 90

Convex mirror

F = E(P) E(P) = E. + E, + E

Using Cis Low to find Edunto sumratric change distributions

1. Use symmetry to estimate (roughly) force of

electric ficld (E) Choose a convenient closed sfa

0 Gaussian sto Apply Gauss's law: •.-4

Solve for ET o-Q/A -- charge density E= q/&A = ole |E| = o 12€, is constant

Ch 19 - Electric Potential

Ch 20 - Electric Current

Moving charges electric current AQ/ At - U = A (Amp)

AV : sometimes denoted as Vor (electromotive foro) a battery

currents are made up of positive, moving charges (opp of electrons)

max potential diffbw terminals of battery: ami

V. ke

ka, ka

not aloctric force doos no W'onaq as it moves on an ouipot sto What is the potential at Point PP F is conservativo (it has a PE) Fl=k (1997) PE =k(99/) in k = 9.99 x 10 Nm If >2 point charges, just add PE's together Electric potential : describes an clectric field (E)

Recall: F= q (V=JIC ar Volts

Capacitance Fsiufal u = 104 AV - APE/a - Wilq dir of E: high V low V APE - -| E||Arcos(e) if Ari E = V = constant Parallel Plata Capacitors: C = KÅ, Id

ESAV/[Arcos()) for point charge: V. -kir E-8.85x10-C /Nm' IF AV = 0 (V = corsan)E0

to t capacitance, put dielectric bw plates

E ric I = 1 EIK CEko E = 10/C) Energy = P = P2 =

AV = IR Ris coefficient of proportionality R= (Ohm) I = CR goes from high V to low

Resistance depends on shape and material of itself V.V. - AEPE / A

Resistivity: inherent property of the material P = AV P-IR PAVIR. P - AqAt() (Watt) For cylindrical conductors for any sufficiently symmetric shapel R= LIA p = resis. Mity of material L = length A = cross-sectional arca wr: battery Connection of Multiple Resistors RR in series: RAR,+R

R. R, in parallell: /R =1/R + 1/R For more complex circuits (multiple currera) Kirchhoff's rules

Junction rule , L

Ch 22 - Electromognetic Induction

Loop rule

EAV = 0 (pot drops = pot rises)

RC Circuits - Charging / discharging capacitors

For multiple branched circuits: Label all the currents w cir's & +/-ends of R's Gotone (or more) equation's) using junction rule Get remaining equations using loop rule

We can choose any loop

We can go around it either CW or CCW If dir. of currents is not obvious, ok to guess If at the end a current is negative, reverse guess

Charging: 0(t) = C4/4 "

Olt ) = CV = 0 Q1t0) = 0

10) = R

VIR - max Discharging: Q/t) - CV

- -

= (V/R) ()

g=.

e 1 9

Current (wo a battery):

B. A orientation of Aw.ct. vector field

Orientation: max if plane blocks 2.0 if plane slices B By construction, B=B+B e: angle bw normal to sfc and B

B. I = 1 B cose Definition: .-1BA OR .-|B|Acose (Weber) Faraday's Love

Aurt person when there is

maten been the coland C .NAD.! At (volt)

the magnet C is like a AV due to a battery Typically we ignore minus sign Lena's Law: I must oppose its cause

through the colchone

This cleaninum Siate the change (0) v precisely Nogate above statement to find (

B B ) Find dir of B

Motional emi' when RHR2 for cir ofl. + side of batary:

7. B. and I are all i

Close switch art=0

(t) = (V/R) (e ) T = RC = time constant Resistors in paralel: same voltage Resistors in series: same current

=&=vBL

Caracters in Scrics & Paralel (Fa) Scrics: 1/ = 110. + 1/C(same mag of a) Parallel C.-C. + C (same voltage)

Voltage is measured b/w 2 points Current is measured through a point

FINAL EXAM CHEAT SHEET

Ch 21 - Magnetic Forces & Fields

Ch 15 - Thermodynamics

FORCES

Magnetic force doos NO work on a charged particla (v stays sovo)

RHRI: determine dir af Fa Cross Product

acting on charged particle AxB is a vector

moving in B1 Definition: AXB|-|A||B sin Direction of Ax B given by RHR1 (F.)

Sweep right hand from A to B to make a fist) & sce where thumb points (toward board in this)

BxAthumb points away from board (toward you

So, AXB- BIA Notation. x into board / page = out of board / page Magnatic Force Lay F = V x B = F = IqV||B | sin() Mass Spectromotor for particles w'a charge of +10 UCM = F = Ft

RHR-2 qVB = mir r=my GB T = 2T (m/qB; Fance on a stright current carming wine lor ist straight current in a |F. I = qvBsino = q (L / tsino |F. I = BILsino Direction: RHR1

=

IF = F, + F + F + F,- 0 ET = NDIA (for N turns)

Aluvays true!

"NIA" - "magnetic moment" (Am) FIELDS Blue to a stright currert carrying wire

Ampere's Law: DPI = p.1 / 2 H. = 411 M 10" TimiA [B] = T (Tesla) Use RHR2 to determine dir of magnetic field lines (B)

Koop fingers curled, point right thumb in

dir. of current, see where curved 4 fingers point Fara bhun 2 straigh: parallel curents 12 images | FI = BI Laine

Direction of F: RHR1 - Find B due toat a point on wire 2

Swoop qvinto B, and B is pointing into the board B| = v.1/2md

Direction towards L (attractive) - Use B from above to find F

- Bat center? F.l= (.1/2rd),

BI=N/2R

1st Law of Thermodynamics - Extension of E-conservation theorem to include heat AU - Q-W U: "Internal energy = total energy (previously E) 0:hear that goes into system

» Of heat ontors system

Oci heat lovos system W: work done by a system

W>0 system does work to environment

W<0 environment does work to system Heal Gas Late PV = nRT

U = 1: LET P: pressure [p] = Pa = N/m

PV Diagram: V: volume M=m

Expansion: VV WO T: temp ITI = Kelvins

Compression: V.<V W O m: number of moles Rideal gas constant = 8.31 J/molk

Constant Pressure Process (sobaric Corsiant Volure Process W=|F|Ar cose

W = 0 no arca under curve W = PAAK A = V

1st low&U=OW W=P AV

AU = 1st law: AU = 0 - W=0 - PAV Constant Templeathermal

Adiabatic Prooss AU = W (wrk done by sys) PV = nRT

Q = 0 (no heat exchange b'w system & enviro) NRT is a constant

Adiabatic compression: V V W CO P = consi/ V

Adiabatic curves are steeper than isothermals W= nRT INVIV)

PV = constant PVS - P.V. AT = T.-T = 0 for an isothermal AU = 32 nRAT 1st law: AU = 0 W=0

= W Molar Specific Heats We can only do this at const VIP

Cons! W

Il PT =0 We want Q = GRÁT

W (adi) = 3/2nRAT 9. - 3/2 R (rue for ideal gases) reminds us of constant volume 1st law: AU = 0

W

A U - Q - BECOMES 3/2nRAT - CAT But, W = 0

So. AU=0 Conse: We want Q = CAT

= 5/2 R

AU = Q - PAV – BECOMES - 1st law: AU=O-W

32 RAT + OBAT NAT = 5/2 nRAT But, W = PAV So, AU = Q-PAV

Hea: Enaires Process whose PV-Diagram is a closed curve heat work AU for an ideal gas in one cycle = ?

Camot Efficiency: a = WIQ: 021 AU -0 = 312 ERAT AT = T.-T = 0

Q = input heat O = output heat st law: U = 0-W = 0

if all input heat was converted to W. e = 1.00 actual efficiency is 1 - Carnot ell think]

AT

Ch 29 - Particles & Waves h = 6.69 x 1011 Js Werk function of metallonat:

W. = smallest art of energy incoded to remove electron E = E. = KE+W. hf = KE,+ W. Photos m = 0 V=C E = hf p = h/A ESP

c = Af Pehla Electrons deBroglio wavelength: -h/P. Wave pattem p/2m = KE Heisarbara Uncertainty Principle 0.0.2h/41 0.

0 0 = 'uncertainties" Notation: x = 0, Ap = 0, Axp2h / 4 Wave Function H P = prab of locating the particle nearrattimet

Ch 30 - Atomic Models clectrically neutral nog charge is easier to extract than + charge electrons axcoute UCM a variable E&B EM waves . charge

loss instability Bahr's Macel (Huatam c doesn't interfere destructively nA = 2 L = n(h / 2) speed of ev, - nh/2mm. distance from a to protoner.h'4'm ke Bohr radius r. = 5.29x10 m smallesir

esimates rof H-atom E. = -(13. Get 1 in)

n=1 ground state n = 21st excited state Photon absotec = E= hf in-1 fn = 4 Photon emcd • E = hf in=4 fi n = 1 OR 2 OR 3

Adiba Expansion / Compression of an Ides Gre PV = P.V. VEic Hent PLITOS

Ch 24 - Electromagnetic Waves

Ch 28 - Special Relativity

Ch 32 - Radioactivity

speed of upropagation of EM waves: c = 1/VE . - 3x 10mis light is an EM wave

Pariacic Waves E.B.cir of propagation for an EM wave Wavelength (Allergih of one cycle (m) Dir of propagation is given by: ExB Period (Tid time for one cycle to pass a fixed point (5) EM waves carry energy

Frequency (f): # of cycles past a fixed point in 1s (1/T or Hz) EM Spectrum 700nm - red 400nm - violc: Paran

Palarized EM wave: E, B don't rotate Law of Polarization: 1 = (1, 2)cos e I is avg intensity of transmitted beam Liis avg intensity of unpolarized incident beam e is blw the directions of the polarization and transmission axes

Galilean Transformation Corccions p = ymy X'=x.vt d'ac-Y t = t

E = yma Wave on a string: Y=[F. (mL)) Lorentz Trarsformation Y = 1 4 - (V10-)) 21 For small sococs y de V-1

Time Dilation - All - Atly At SA: O' is the one where the 2 events that define At, Al' occur at same location LOCz Contraction - L'=YL Y 21 **There's only contraction along the way it's moving" O' is the rest frame of the object "Moving objects contract in direction of motion"

Z = of protons (atomic #) - D's clemen: N = number of routrons (neutron #) ANN+Z isotopes have samo Z but different A size of nucleus r-1.2.10 m Puchar (nuclear density) - 2.3x10 kg/m Tuses of Radiati a decay: 2p 2- Z-Z-2 A-A-4

decay: n po Z.Z+1 AA Y decay: EM wave/photon of high f AN / AI ANN (t) = N * T In(2)/A Carton Dating The = 5730 yrs for NCINC -1.310 assumed const

FINAL EXAM CHEAT SHEET

Constants speed of light = C 3 x 108 m/s R: ideal gas constant = 8.31 J/mol K air - vacuum, sonar - 1 charge of electron e = 9.11x10-31 kg mass of electron = 1.60x10-19 C k= 8.99x109 Nm2/C2 E. = 8.85x10-12 CZ/Nm2 Ho = 411 X 10-7 Tm/A speed of u propagation of EM waves:

c=11 VEOHO ~3x 108 m/s y = 1/ (1 - (v2/c)) 2 1 h = 6.63 x 10-34 Js h = 6.63 x 10-34 Js 1 ev = 1.6x10-19 J Pnuclear (nuclear density) - 2.3x1017 kg/m3 nuclear radius: r- 1.2x10-15 m N4C/N2C -.3x10-12 assumed constant

References: